Mr. Jean, 26, was taken to a hospital, where he was pronounced dead.

Officer Guyger was placed on administrative leave but was not immediately arrested, and the Dallas Police Department handed the investigation over to the Texas Rangers, the state’s top law enforcement agency. The Texas Rangers announced the arrest on Sunday night but declined to provide details about the case.

A lawyer for Officer Guyger could not be reached for comment on Sunday. The Dallas Morning News reported that she could be heard on a 911 call crying and apologizing. “I’m so sorry,” she said.

Lee Merritt, a lawyer for Mr. Jean’s family, said in an interview late Sunday that Officer Guyger’s arrest was a “step in the right direction.” But he questioned why the authorities had waited, saying, “We don’t want it lost on anyone that, had this been a regular citizen, she would have never left the crime scene.”

Officials have not said how Officer Guyger may have mistaken the apartment for her own, or what interaction she had with Mr. Jean just before the shooting.

In an interview with CNN on Sunday, Mayor Mike Rawlings of Dallas called the case “bizarre” and “confusing to all of us.” He said that Officer Guyger apparently parked her car on the wrong floor of the building’s parking lot and then walked to the apartment. “We don’t know how she got into that door,” he said. “We have to get to the bottom of this for everybody.”