Dallas police Chief Renee Hall said Saturday that the Rangers had asked her to hold off on a planned manslaughter charge while their investigation is underway, FOX 4 of Dallas reported.
Chief Hall said in the interest of being as transparent as possible, she has invited the Texas Rangers to take over the investigation.
Officer Amber Guyger was arrested Sunday on a manslaughter charge and later released on bond.
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.
Jean's death has renewed calls for policing reform and places the national spotlight back on a police department that, just two years ago, lost five of its officers in a shooting.
"Dallas cop mistakes someone's else apartment for hers and shoots the tenant DEAD".
She says going forward the group expects transparency and accountability in the case.
In a statement Mr Hall said: "We are continuing to pray for Mr Jean's family and ask that the community remain patient as this investigation is conducted". Guyger has been a part of the department for four years and is assigned to the Southeast Patrol Division.
Guyger hadn't been questioned when Hall spoke early Friday afternoon, and Hall said no information was available about Guyger's level of fatigue at the time of the shooting. Guyger shot and injured the suspect, according to the department's statement.
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The news of Guyger's arrest broke on the evening of September 9, 2018 after two days of confusion about whether Guyger, 30, would face charges in the freaky shooting death of Botham Shem Jean, a Saint Lucian man who moved to America to attend a Christian college and later got a job in risk assessment for a prominent company in Dallas. A struggle began and Ms Guyger fired her Taser at Perez, who then wrested it away from her. Online records show that Amber Guyger has long ties to Texas and is 30-years-old.
An attorney for Jean's family has insisted that the officer be charged and treated like any other member of society.
Jean's mother, Allison, suggested in an interview on Friday that her son might still be alive if he was white.
Funeral services for Jean are scheduled for 11 a.m. Thursday at the Dallas West Church of Christ, which Jean attended.
At a press conference Sunday, before the arrest was announced, the attorneys representing Jean's demanded action be taken against the officer, arguing that a police officer should not be given preferential treatment. Hall did not say why the officer opened fire and declined to discuss what she may have been doing before she returned home after working a full shift Thursday.
"There are more questions than we have answers", she said. If it was a white man would it have been different? "Botham loved everyone, and everyone loved him".
Police called the situation "very unique" and said Guyger was tested for drugs and alcohol afterward.