Body cam footage shows the officer shooting within seconds of seeing her.
The man who called police, James Smith, 62, said he was trying to be a good neighbour after noticing Ms Jefferson’s front door was open and her lights were on.
“If I had never dialled the police department, she’d still be alive.” Mr Smith told local media. “It makes you not want to call the police.”
Allegations of police brutality in black communities have been a longstanding issue in the US.
In its initial statement, the Fort Worth Police Department said the officer had “perceived a threat” when he drew his weapon.
Earlier Ms Jefferson’s sister, Ashley Carr, said she had been “killed by a reckless act” and called for a federal investigation.
Lee Merritt, a civil rights lawyer who is representing the family, said: “The investigation should be handled by someone other than the Fort Worth Police Department.”
He added that the department was “on track to be one of the deadliest police departments in the United States”.
Accurate data on police shootings is difficult to obtain since local police forces are not obliged to provide figures.
According to a database compiled by the Washington Post, 709 people have been killed by law enforcement officials so far this year and about 20% of victims were black. Texas had the second-highest number of total deaths.
Fort Worth residents held a protest outside Ms Jefferson’s home on Sunday evening. First planned as a vigil, the gathering became a demonstration as residents demanded justice for the 28-year-old victim.
Participants held candles and chanted: “No justice, no peace.”
“State sanctioned violence has always been a culture for black people,” said protester Michelle Andersen. “It’s not about a training issue.”
Fort Worth Mayor Betsy Price was present at the vigil, but left after she was approached by protesters shouting “lock him up”, in reference to the officer, CBS News reported.
What happened on Saturday?
The shooting happened at about 02:30 local time (07:30 GMT).
The body cam footage of the incident shows police searching the perimeter of Jefferson’s property, before noticing a figure at the window. After demanding that the person put their hands up, an officer then fired through the glass.
Ms Jefferson had been playing video games with her eight-year-old nephew before she went to investigate the noise outside the window and was shot, said a lawyer representing her family.
The officers involved did not park their marked cars in front of her house and did not identify themselves as police, officials said.
Ms Jefferson’s killing comes two weeks after Dallas police officer Amber Guyger, 31, was found guilty of murdering 26-year-old Botham Jean.
Last year Guyger shot and killed Jean as he sat eating ice cream on his apartment sofa, less than 35 miles (55km) from Saturday’s incident.
Guyger testified she mistakenly thought she was in her own flat and believed Jean to be an intruder.
At trial, Guyger admitted to shooting “an innocent man”.