Authorities announced that Aaron Dean, 34, was booked into jail on a murder charge on Monday afternoon. The police chief said earlier he had acted without justification and would have been fired if he had not taken the decision to resign.

Police bodycam video showed Mr Dean approaching the door of the home where Atatiana Jefferson, 28, was caring for her 8-year-old nephew early on Saturday. He could then be seen walking around the side of the house, pushing through a gate into the fenced-off backyard and firing through the glass.

Mr Dean, who is white, was not heard identifying himself as police on the video, and interim police chief Ed Kraus said there was no sign Mr Dean or the other officer who responded, even knocked on the front door.

“Nobody looked at this video and said that there’s any doubt that this officer acted inappropriately,” Mr Kraus said.

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Earlier in the day, Jefferson’s family had demanded that Mr Dean, a member of the force for 17 months, be fired and arrested.

“Why this man is not in handcuffs is a source of continued agitation for this family and for this community,” family attorney Lee Merritt said.

Police went to Ms Jefferson’s home about 2.25am after a neighbour called a non-emergency line to report a door being ajar. In a statement, the department said officers saw someone near a window inside the home and that one of them drew his gun and fired after “perceiving a threat”.

The video showed Dean shouting: “Put your hands up! Show me your hands”. He then began to start firing.

Texas police walk black man tethered to a horse

Ms Jefferson was staying up late, playing video games with her nephew, when she was killed, according to the family’s attorney.

Asked what caused the officer to open fire, the police chief said: “I cannot make sense of why she had to lose her life.”

He said Mr Dean resigned without talking to internal affairs investigators.

The video included images of a gun inside a bedroom. Mr Kraus said he did not know whether Ns Jefferson was holding the weapon. But he said the mere fact she had a gun should not be considered unusual in Texas.

“We’re homeowners in Texas,” the police chief said. “Most of us, if we thought we had somebody outside our house that shouldn’t be and we had access to a firearm, we would be acting very similarly to how she was acting.”

Mr Kraus said releasing the images of the weapon was “a bad thing to do”.

Mayor Betsy Price called the gun “irrelevant”.

“Atatiana was in her own home, caring for her 8-year-old nephew. She was a victim,” said Ms Price.