The police had been called at least twice before to Ms. Danner’s apartment in the Castle Hill neighborhood of the Bronx. One time she had barricaded herself inside, forcing the authorities to break down the door. Another time she had threatened to jump out a window.

She feared death at the hands of the police, her relatives said. She had even written a six-page essay about her illness to a lawyer that mentioned Ms. Bumpurs. “We are all aware of the all too frequent news stories about the mentally ill who come up against law enforcement instead of mental heath professionals and end up dead,” she wrote.

The street protests and publicity surrounding the shooting prompted Sergeant Barry to ask a judge to move the trial to another town, but the motion was denied. Now he has waived his right to a jury and put his fate in the hands of Justice Robert A. Neary.

Sergeant Barry’s lawyers plan to argue he acted in self-defense. According to his account related in court papers, he arrived at the apartment on Pugsley Avenue on Oct. 18, 2016, to find four officers standing in the living room and Ms. Danner, who was 5-foot-7 and 233 pounds, sitting on a bed in her room, snapping a pair of scissors and cutting paper. The police had learned from a 911 caller and from Ms. Danner’s sister that she was a paranoid schizophrenic.

Image Deborah Danner, 66, a schizophrenic woman, was shot and killed by a police sergeant in 2016 after picking up a bat in the bedroom of her Bronx apartment. Credit...

Sergeant Barry says he talked Ms. Danner into putting the scissors on a nightstand and coaxed her to the doorway of the room. But she refused to come further.

Then, he motioned to another officer and together they tried to grab her. She retreated into her room and pulled a baseball bat from under the blankets on her bed, according to his account. The sergeant and a second officer went into the room after her. She raised the bat as if she were stepping to the plate. Sergeant Barry pulled his gun and told her more than once to drop the bat. She swung it at his head. He fired twice into her torso.