Atatiana Jefferson was killed after a neighbour in Fort Worth phoned police to say he was worried because the 28-year-old’s front door had been left open.
In body cam footage released by the police, two responders can be seen using flashlights to search the home from outside before one is heard shouting through a window: “Put your hands up, show me your hands.”
A shot is then fired.
Ms Jefferson was pronounced dead at the scene in the early hours of Saturday. Her eight-year-old nephew is understood to also have been in the house at the time.
In a statement, Fort Worth Police Department said the officer fired the single shot after “perceiving a threat” inside the property.
The body cam video also included images of a gun inside the residence, but it is unclear if the firearm was found near the woman.
The shooting officer, who has been on the force since April 2018, has been placed on administrative leave pending an investigation.
James Smith, the person who initially called police, said he had just been trying to be a good neighbour.
He told the Fort Worth Star-Telegram newspaper: “I’m shaken. I’m mad. I’m upset. And I feel it’s partly my fault. If I had never dialled the police department, she’d still be alive.”
Mr Smith said Ms Jefferson and her nephew lived at the address with an older woman, who had been in the hospital.
“It makes you not want to call the police department,” he added.
Pastor B.R. Daniels Jr, a local activist, said at a press conference hours later that the police must stop “shooting first, asking questions later”.
He said: “We want a review of policy, procedures.
“How do you storm a house, kill a young lady, with an 8-year-old minor in the house, who could have been killed himself?”
Authorities said the body cam footage had been released to provide transparency but any video taken inside the house could not be distributed due to state law.