The lawyer for the family of a man who was shot dead at his home by a Dallas police officer is calling for her to be arrested and charged, saying the fact that she remains free days after the shooting shows she is receiving favorable treatment.

S Lee Merritt, who is representing the family of 26-year-old Botham Jean, said the family was not calling on the authorities to jump to conclusions or to deny officer Amber Guyger her right to due process.

But Merritt, flanked by members of the family and Mothers Against Police Brutality, said they want Guyger “to be treated like every other citizen, and where there is evidence that they’ve committed a crime, that there’s a warrant to be issued and an arrest to be made”.

Guyger, a four-year veteran of the police force, had not been charged as of Sunday morning, according to city of Dallas and Dallas County online records. The police department released her name on Saturday night, two nights after she shot and killed Jean.

Police chief U Renee Hall said the day after the shooting her department was seeking manslaughter charges against Guyger. But she said on Saturday the Texas Rangers, which has taken over the investigation, asked her department to hold off because it had learned new information and wanted to investigate further before a warrant was issued.

Police on Sunday morning referred questions to the Rangers. Phone messages seeking comment were not returned.

According to police, Guyger shot and killed Jean after returning in-uniform to the South Side Flats, where they both had apartments, following her shift. She reported the shooting to dispatchers and told officers who responded she had mistaken Jean’s apartment for her own.

Many questions remain about what led Guyger to shoot Jean. Hall said the officer’s blood was drawn at the scene so it could be tested for alcohol and drugs. Investigators have not released the results of those tests.

Jean’s mother, Allison Jean, wondered whether race could have been a factor. Her son, who grew up in the Caribbean island of St Lucia before attending college in Arkansas, is black. Guyger is white.

“If it was a white man, would it have been different? Would she have reacted differently?” Allison Jean said on Friday.

Jean was not the first person shot by Guyger. She shot another man, Uvaldo Perez, on 12 May 2017, while she was on duty.

According to an affidavit in the case filed against Perez, police were looking for a suspect when Guyger and another officer were called to assist a third. Perez got out of a car and became combative with Guyger and another officer. A struggle began and Guyger fired her Taser at Perez, who wrested it away from her. She drew her gun and fired, wounding Perez in the abdomen. Guyger was not charged in the shooting.

Sgt Mike Mata, who heads Dallas’ largest police union, the Dallas Police Association, called on Saturday for an “open, transparent and full investigation” of the event, the Dallas Morning News reported. He described Jean as an “amazing individual” and said “if the grand jury deems necessary, this officer should have to answer for her actions in a court of law in Dallas county”.

Friends and family gathered at the Dallas West Church of Christ to remember Jean, who had been working for accounting firm PwC since graduating in 2016 from Harding University in Arkansas, where he often led campus religious services. They described Jean as a devout Christian and a talented singer.

“Botham did everything with passion,” Allison Jean told the prayer service. “God gave me an angel.”

His uncle, Ignatius Jean, said the killing has devastated the family and left it searching for answers.

“You want to think it’s fiction … and you have to grapple with the reality,” he said.