USviewer: The Bronx Borough President Ruben Diaz Jr called the shooting an "outrage."
It follows a string of incidents that have put law enforcement across the country under heightened scrutiny over the use of lethal force, especially against minorities and the mentally ill.
Police on Tuesday evening received an emergency call of an emotionally disturbed person at an apartment building in the Bronx, where the woman's neighbor complained she was acting irrationally, said New York police assistant chief Larry Nikunen.
The sergeant entered the woman's apartment and found her clutching scissors in a bedroom, Nikunen said at a news conference.
The sergeant talked to the woman, convincing her to put down the scissors, but she charged toward him while picking up a baseball bat, Nikunen said.
"As she attempted to strike the sergeant he fired two shots from his service revolver, striking her in the torso," Nikunen told reporters.
The New York Police Department is investigating and will look into why the sergeant did not use a Taser against the woman instead of opening fire, Nikunen said.
The name of the woman, who was pronounced dead at a hospital, was not immediately released. Police had previously been to her apartment to handle similar disturbances, Nikunen said.
Nikunen did not give the races of the officer or the woman in his statement to reporters.
Bronx Borough President Diaz, a former state lawmaker, called in a statement for the state attorney general to investigate the shooting of the woman, whom Diaz called "mentally disturbed."
"This elderly woman was known to the police department, yet the officer involved in this shooting failed to use discretion to either talk her down from her episode or, barring that, to use his stun gun," Diaz said. "That is totally unacceptable."
A representative for the New York police officers' union could not be reached for a comment late on Tuesday.
In a California shooting last month that sparked protests, an officer in El Cajon responding to a report of a man acting erratically shot him to death. Police said the man had pointed an object, later determined to be a vaping device, at the officer.