(CNN) A former Catholic priest faces a first-degree murder charge for allegedly killing a onetime beauty queen who was last seen alive the night he heard her confession.

John Feit, 83, had long been the main suspect in the 1960 death of schoolteacher Irene Garza, but he wasn't arrested until Tuesday in Scottsdale, Arizona.

According to an indictment unsealed Wednesday, a grand jury in Hidalgo County, Texas, decided there was enough evidence to charge that Feit, "with malice aforethought, (caused) the death of Irene Garza by asphyxiation in a manner and means unknown to the grand jury."

Garza was last seen alive the night before Easter 1960, when Feit heard her confession at Sacred Heart Catholic Church in McAllen, Texas. Five days later, searchers found the body of the 25-year-old former Miss South Texas facedown in a canal.

In 2004, a grand jury heard the case but decided not to indict Feit. Authorities haven't released details about what's changed since then.

"At this point I am being very careful about what information I'm giving out there," Hidalgo County District Attorney Ricardo Rodriguez told CNN about his decision to present the case to the grand jury again, and the outcome.

"All I can say at this point is that we've had about a year and two months to start and look through this case," he said. "We had the facts and evidence to proceed."

Indictment of ex-priest John Feit for murder of #IreneGarza unsealed: "asphyxiation in a manner and means unknown" pic.twitter.com/2VJEHcAvLv — Mariano Castillo (@marianoCNN) February 10, 2016

In a sworn statement to authorities and during an interview with CNN in 2013, Feit denied he killed Garza.

Feit told police Garza left the rectory after he heard her confession and the last time he saw her, she was standing outside the church.

'This whole thing makes no sense'

Feit said Wednesday that he would fight extradition to Texas. He's behind bars in Maricopa County, Arizona, where a judge set his bond at $750,000.

Feit used a walker to steady himself as he approached the podium during his first court appearance Wednesday. He told the judge he was puzzled.

"This whole thing makes no sense to me, because the crime in question took place in 1960," he said.

Investigators came to Arizona and questioned him extensively in 2003, he said.

"That was 13 years ago," he said. "I'm totally puzzled by something coming up now, after the fact."

Rodriguez said authorities will keep pushing for Feit's extradition.

"We are working to make sure he comes back to Hidalgo County to stand trial so justice can be served and Ms. Garza's family can have closure," the prosecutor said in a written statement released Wednesday evening. "We will elaborate further with additional details once we have completed the extradition process."

The case that shook a city

An autopsy determined Garza had been raped while in a coma and then died from suffocation. Near Garza's body investigators found items that belonged to the church, including a candelabra.

When John Feit was a 27-year-old Roman Catholic priest, he was questioned in Garza's killing.

One item, a metallic Kodak slide photo viewer, belonged to Feit, at the time a 27-year-old priest who was assigned to the church.

Questioned by police, Feit failed polygraph tests.

What also made police suspicious was that 24 days before the killing, Feit had been arrested for attacking another young woman at a church in a town about 10 miles from McAllen.

Feit pleaded no contest to misdemeanor aggravated assault. A judge found him guilty and fined him $500 with no prison time.

Sacrilegious

The crime shocked the people of McAllen. It was unthinkable that a Catholic priest would commit such a crime. That's the way Garza's cousins remember it.

"We were accusing a priest that -- in those days priests were infallible, " said Lynda De La Vina, who was 9 years old at the time.

Another cousin, Noemi Sigler, was only 10 when Garza was killed. "It was impossible for a priest to do such a deed. I mean, if you thought of it, that would be sacrilegious."

But Feit was the likely suspect, said former Texas Ranger Lt. Rudy Jaramillo, who started investigating the murder in 2002 when he served with a Rangers cold case unit. The evidence, he said, "suggests and indicates that that's who it's pointing to."

Garza cousin: It was 'a cover-up'

Authorities at the time protected Feit, said Sigler. "I don't know whether it was out of respect for the church or anger or fear, I have no idea," she said. Shortly after the killing, the church transferred Feit far away to a monastery. He would be moved to other locations over time, and about three years after the killing, the church transferred Feit to Our Lady of Assumption monastery in Ava, Missouri.

Sheltering Feit "was about protecting the church and somehow believing that the church takes care of their own," said De La Vina. "It was the best that could have happened at that point. Because nothing else was being done."

Sigler describes her view in more succinct terms: It was "a cover-up."

Photos: Crime scene evidence Photos: Crime scene evidence Beauty and the priest: Crime scene evidence – On April 16, 1960 -- the day before Easter -- schoolteacher and former beauty queen Irene Garza, age 25, went to confession at her family's church in McAllen, Texas. She never came home. On Easter, her father filed a police report that his daughter was missing. Click through this gallery to see evidence and crime scenes in Garza's still unsolved death. Hide Caption 1 of 19 Photos: Crime scene evidence Beauty and the priest: Crime scene evidence – Garza was crowned Miss South Texas in 1958. Employed as a second-grade teacher at an elementary school, Garza had a way with children, family members recall. She also was blessed with a musical voice and a natural effervescence. Hide Caption 2 of 19 Photos: Crime scene evidence Disturbing clues – After Garza went missing, family, friends and neighbors formed search parties. That's how many of her belongings were found, including this beige ladies shoe that had been thrown into a field. Hide Caption 3 of 19 Photos: Crime scene evidence Her patent leather handbag – Searchers also found this patent leather handbag, which belonged to Garza. "It started escalating, knowing that when they found these things, something was definitely wrong," remembered Garza's cousin, Lynda de la Vina, who was 9 at the time. Hide Caption 4 of 19 Photos: Crime scene evidence The canal – Five days after she disappeared, police found Garza's body face down in this McAllen canal. An autopsy report states that her body showed evidence of "recent trauma, sexual intercourse" and "trauma to the head." According to the report, "evidence of strangulation could not be found, but suffocation could have been carried out by placing a cloth over the mouth and nose." "The subject was dead when placed into the canal," the report said. Hide Caption 5 of 19 Photos: Crime scene evidence Garza's blouse – Police evidence in the investigation included Garza's blouse, seen here. Garza's death certificate states that her cause of death was "trauma to the right side of her head" causing "hemorrhage of the brain" and "suffocation." Hide Caption 6 of 19 Photos: Crime scene evidence Garza's petticoat – The death certificate also states that Garza's body "bore evidence of having been raped ... while in a coma." Hide Caption 7 of 19 Photos: Crime scene evidence Garza's skirt – De la Vina remembers how the family reacted when they heard the news that Garza had been found dead. "The one thing I remember is just screams," she recalled. "Screams from my aunt, screams from my mother. Everybody screaming." Hide Caption 8 of 19 Photos: Crime scene evidence Metallic slide photo viewer – Next to Garza's body, police found this heavy Kodak metallic slide photo viewer, said former McAllen police officer Sonny Miller, who supervised crime scene investigations in 1960. Miller said investigators eventually learned the viewer belonged to the Rev. John Feit, a 27-year-old priest at Garza's church, Sacred Heart Catholic Church.

Hide Caption 9 of 19 Photos: Crime scene evidence John Feit – Just 24 days before Garza's killing, Feit had been arrested for attacking another young woman at a church in a town about 10 miles from McAllen. Feit pleaded no contest to misdemeanor aggravated assault. A judge found him guilty and fined him $500 with no prison time. At the time of Garza's killing, Feit was assigned to Sacred Heart. Hide Caption 10 of 19 Photos: Crime scene evidence Sacred Heart Catholic Church – After her body was found, Garza's car was still parked at Sacred Heart, so that's where police first focused their investigation. Hide Caption 11 of 19 Photos: Crime scene evidence The church rectory – Feit acknowledged to police that he heard Garza's confession in the church rectory on the day she went missing. He told police she left. Feit was the last man known to see Garza alive. Although he has never been charged, police officers and law enforcement agencies that have dealt with the case say they believe Feit killed Garza. Hide Caption 12 of 19 Photos: Crime scene evidence The crusader – in 2002, then-Texas Ranger Rudy Jaramillo spoke to two witnesses who offered stunningly similar stories key to Garza's slaying. One was a priest, the other a monk. They both said Feit had admitted to them that he had killed Garza. Hide Caption 13 of 19 Photos: Crime scene evidence Former priest Feit speaks – Feit left the priesthood in the late 1960s. Now in his 80s, Feit lives in a pleasant neighborhood in Phoenix. He's married with a daughter and grandchildren. In 2007, CNN's Gary Tuchman asked Feit: "Did you commit the murder of Irene Garza?" Feit answered, "Interesting question. The answer is no." Hide Caption 14 of 19 Photos: Crime scene evidence Prosecuter says charges wouldn't stick – Rene Guerra, the criminal district attorney for Hidalgo County, Texas, said he couldn't rely on the information from the two new witnesses who had come forward in the case -- the priest and the monk. When a grand jury heard the case in 2004, neither witness testified. The grand jury decided against indicting Feit. Does Guerra think Feit is the killer? "Everything points to him," said Guerra. Does he think there's enough evidence to convict Feit in a trial? "I honestly don't." Hide Caption 15 of 19 Photos: Crime scene evidence 'New eyes' – De la Vina has been fighting for years to get Feit charged. If a new district attorney is elected, "they would come in with new eyes, a new attitude and -- hopefully see the things that we saw and the injustices that we saw years ago." Hide Caption 16 of 19 Photos: Crime scene evidence 'I said no' – Another of Garza's cousins, Noemi Sigler, was 10 at the time of the killing. For decades she has been researching and cataloging information to push authorities toward charging Feit. When Sigler started her crusade, she said police dismissed her. "Literally I was told, 'That's an old case,' kind of like, 'leave it be.' And I said, 'no, no,' to myself, 'no.'" Hide Caption 17 of 19 Photos: Crime scene evidence 'Voice from the grave' – "I want to give her a voice from the grave. I really do," said Sigler. "And she wants it. She is here. And she wants justice." Hide Caption 18 of 19 Photos: Crime scene evidence 'I wanted justice for her' – Jaramillo, now a security company executive, still keeps a framed photo of Garza on a shelf behind his desk. "I honor her because of the type of person she was, you know. She was loved by everybody in the valley." Jaramillo still hopes Feit will be arrested someday for Garza's killing. "I wanted justice for her," he said. "And it didn't happen." Hide Caption 19 of 19

During the next four decades, the case grew colder and eventually faded from the headlines. But the cousins kept pushing until 2002, when the Rangers and Jaramillo reinvigorated the investigation.

Hopes for solving the case were never higher when two surprise witnesses independently come forward, each separately claiming that they heard Feit confess.

But then-District Attorney Rene Guerra delayed bringing the case before a grand jury for years, saying their testimony wasn't credible.