Police believe the triple homicide of a Muslim family in their North Carolina home was due to a parking conflict and was likely not religiously motivated. But the victims’ family disagrees, calling it a “hate crime” and an “execution.”

READ MORE:Chapel Hill shooting: 3 Muslims gunned down in N. Carolina

The three young relatives in the college town of Chapel Hill were gunned down in their home on Tuesday evening. The victims in the triple homicide have been identified as Deah Shaddy Barakat, 23; his wife, Yusor Mohammad Abu-Salha, 21; and her sister, Razan Mohammad Abu-Salha, 19. All three victims were shot in the head.

A 46-year-old man identified by police as Craig Stephen Hicks turned himself in late Tuesday night. He was subsequently arrested on suspicion of three counts of first degree murder. Hicks lived next door to the family in a condominium complex a few miles east of the University of North Carolina’s flagship campus.

RT @AlvarezABC11:Chapel Hill Police on scene of shooting here on Summerwalk Circle, on scene now, waiting for details pic.twitter.com/b9OkDHPxRR — ABC11 EyewitnessNews (@ABC11_WTVD) February 10, 2015

The women’s father, psychiatrist Dr. Mohammad Abu-Salha, told the Raleigh News & Observer that, while parking may have been the catalyst for Tuesday’s events, the shooter had an underlying animosity towards his daughters and son-in-law based on their religion and culture.

“It was execution style, a bullet in every head,” Abu-Salha said Wednesday morning. “This was not a dispute over a parking space; this was a hate crime. This man had picked on my daughter and her husband a couple of times before, and he talked with them with his gun in his belt. And they were uncomfortable with him, but they did not know he would go this far.”

The grieving father said that one of his daughters had told the family a week ago that she had a “hateful neighbor.”

“Honest to God, she said, ‘He hates us for what we are and how we look,’” he said. Both women wore hijabs, the traditional Muslim head scarf.

Hicks is a self-described atheist who regularly posted content critical of religion on his Facebook account.

Suzanne Barakat, older sister of Deah is asking authorities to investigate the #ChapelHillShooting as a hate crime. pic.twitter.com/TIzLlhau7S — Eileen Park (@EileenParkTV) February 11, 2015

While police noted Wednesday morning that the killings were likely part of an ongoing parking dispute, they added that they have not ruled out the possibility that it was a religiously motivated attack.

“Our investigators are exploring what could have motivated Mr. Hicks to commit such a senseless and tragic act,” Chapel Hill Police Chief Chris Blue said in a statement. “We understand the concerns about the possibility that this was hate-motivated and we will exhaust every lead to determine if that is the case.”

Durham District Attorney Roger Echols also said that law enforcement has not eliminated any motives at this point.

"All motives will be under investigation," Echols said, according to WRAL.

Hicks' wife Karen denied that her husband was motivated by Islamophobia, but rather by the parking situation at the condominium complex.

Karen Hicks, wife of #ChapelHillShooting suspect says the murders had nothing to do with religion. @WNCNpic.twitter.com/5Aaco5NUXe — Justin Quesinberry (@JustinQberry) February 11, 2015

"This incident had nothing to do with religion or the victims’ faiths," Hicks’s wife told reporters at a news conference Wednesday afternoon.

She added that the shooting came as a "complete shock" and she expressed her "deepest sympathy and condolences" to the victims’ families, WTVD reported.

Hicks’ attorney also stressed that the family does not believe the shooting was a hate crime.

"It has nothing to do with terrorism. It has nothing to do with anything but the mundane issue of this man being frustrated day in and day out and not being able to park where he wanted to park," said attorney Rob Maitland. "These victims were there at the wrong time and wrong place."

Both Karen Hicks and Maitland mentioned mental illness as a factor.

Atty for #ChapelHillShooting Suspect's Wife: Murders motivated by parking. Raises awareness about mental illness. pic.twitter.com/OPa3sD7r6C — Tamara Gibbs ABC11 (@TGibbsABC11) February 11, 2015

Parking was a recurring issue between Hicks and his three victims, but it never escalated to the point of involving law enforcement, Chapel Hill police told WTVD.

“I talked with the brother of Deah Barakat who was shot, and he told me that allegedly this neighbor had gone into this apartment before, over parking, and this was an issue that they had dealt with in the past,” WUNC’s Reema Khrais reported.

On Tuesday evening, one 911 caller heard eight shots; another reported between five and 10 shots after she heard “kids screaming,” according to released recordings of the calls. Neighbors have described the parking situation as “confusing,” WRAL reported.

Neighbors say parking at condo where #ChapelHillShooting occurred is confusing. Here's a notice posted about towing pic.twitter.com/Pg9PVqe6a0 — Arielle Clay (@AClayNews) February 11, 2015

While many across social media and in the Muslim-American community called on law enforcement to investigate the incident as a hate crime, local officials sought to calm fears of an outbreak of violence against those who practice Islam.

"The events of yesterday are not part of a targeting campaign against Muslims in North Carolina," US Attorney Ripley Rand told reporters at a news conference Wednesday afternoon, adding that there is "no information this is part of an organized event against Muslims."

"This appears, at this point, to be an isolated incident," Rand said.

The Council on American Islamic Relations (CAIR) called on federal authorities to investigate the slayings and address a “possible bias motive” for them.

READ MORE:#MuslimLivesMatter: Shock and outrage as 3 Muslim students gunned down in N. Carolina

"Based on the brutal nature of this crime, the past anti-religion statements of the alleged perpetrator, the religious attire of two of the victims, and the rising anti-Muslim rhetoric in American society, we urge state and federal law enforcement authorities to quickly address speculation of a possible bias motive in this case," said CAIR National Executive Director Nihad Awad, according to WTVD.

Currently, federal law authorities are assisting “merely in a monitoring capacity at this point," Rand said. They are helping process evidence, which is standard in homicide cases, WRAL reported.

Hicks was arraigned Wednesday morning. Durham County Judge Marcia Morey denied bond, and scheduled his next court appearance for March 4. Hicks was originally being kept at the Durham County Jail, but was later moved to the state’s Central Prison. Authorities have not elaborated on why.

Candlelight vigil tomorrow night 6-8 p.m. NCSU Brickyard. Open to the community. #ChapelHillShootingpic.twitter.com/XkpnEGE8Mt — College of Design (@NCStateDesign) February 11, 2015

Vigils for the victims are planned at UNC and at North Carolina State University, where all three received their undergraduate degrees.