The shooting sparked major outrage on social media and widespread calls for Guyger's arrest.
When officers initially responded to the scene, they began investigating the case as an officer-involved shooting, Hall said.
The lawyer for the family of a Texas man who was gunned down 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's receiving favourable treatment.
Mr Jean's mother, Allison, said in an emotional statement that the police officer: "Has to face whatever the law says". Perez got out of a vehicle and became combative with Guyger and another officer. "The very Bible says to render to Caeser that which is Caeser so if Ceaser says to pay a penalty for a life, then she has to pay".
She posted $300,000 (£232,000) bail, ABC reported, and has been released.
Jean will be buried in St. Lucia on Thursday, according to WFAA.
Merritt, who represents the family of Antwon Rose II, an unarmed teenager who was shot by an East Pittsburgh police officer, said race and police's use of force are deeply intertwined in this country. The statement also indicated, "They made the decision to postpone pursuing a warrant until they could follow up on information that they received from the interview with the officer".
Richard Healy Nelson, who lives in the apartment building where the shooting took place, told KDFW-TV the incident was unnerving.
The prayer vigil Saturday, attended by dozens of people including Jean's mother, was held at the Dallas West Church of Christ.
She said blood samples have been taken from the officer and will be tested for drugs and alcohol. He was transferred to a hospital and died later that evening. Rawlings called Jean "a great man" and "exactly the kind of citizen we want to have in the city".
"Our first & foremost priority will be to ensure justice is served for this family".
As Law&Crime's Alberto Luperon reported on Friday, preliminary information suggested that the officer came home in uniform after working a full shift.
The Department of Public Safety, which oversees the Texas Rangers, didn't immediately reply to a Saturday phone message seeking comment about the investigation. It's unclear what the interaction was between them, but at some point she "fired her weapon, striking the victim", according to Hall.
Jean was a businessman born in St. Lucia, a Caribbean island nation where he and his family held positions in government.
The St Lucian government issued a statement expressing "shock" at the killing and said officials at its embassy in the United States would provide assistance to the family.
A police spokeswoman referred questions to the Texas Ranger Division. Guyger, who reportedly has been a cop for four years, alleges to have mistaken the victim's home for her own.
Dallas police had said previously that it's believed Guyger mistakenly went to Jean's apartment, thinking it was her own, but that's a story that has sparked outrage and disbelief on the Internet and also from Jean's family.