Many drew parallels between Ms. Jefferson’s death and the killing of Botham Jean, a black accountant who was shot to death by a white off-duty police officer in his Dallas apartment last year. The officer in that case, Amber Guyger, was fired, and this month was convicted of murder and sentenced to 10 years in prison.

Ms. Jefferson’s mother had followed Ms. Guyger’s trial closely and had seen Mr. Merritt on television representing the families of Mr. Jean and a witness, the lawyer said.

The Police Department has not named the officer, but said in a statement that he had perceived “a threat,” although a spokesman declined to elaborate. The officer had been with the department since April 2018 and has now been placed on administrative leave.

Lt. Brandon O’Neil, a department spokesman, said at a news conference that the department was continuing to investigate the shooting, and would look at why the officer did not identify himself as a police officer. The officer is scheduled to be interviewed by the department’s major case unit on Monday.

Officers tried to provide medical care, but Ms. Jefferson was pronounced dead by 3:05 a.m., according to the Tarrant County medical examiner. Police said they had found a gun in the room — not the one the officer used — but have declined to answer further questions.

“Law enforcement has not said that she wielded a weapon,” Mr. Merritt said, adding that she owned a gun legally. “Also, it wouldn’t matter, because that’s her home.”

Kelly Allen Gray, a city councilwoman who represents the neighborhood where Ms. Jefferson was killed, said it did not make sense that a neighbor’s concern could lead to a woman’s death.