It happened again on Monday afternoon in New York City: An armed person who appeared to be in the throes of a psychiatric crisis committed a violent act and moved toward the police, who then opened fire.

In this case, it was a 49-year-old woman with two kitchen knives who attacked two people, one fatally, before the police shot and killed her in Times Square in Manhattan.

Often, such incidents lead to intense scrutiny of the police response and a debate over whether the deadly confrontation could have been avoided.

In interviews on Tuesday, several law enforcement experts said that the shooting was justified. But they questioned some of the actions by the officers leading up to it, saying they might have put the public or the officers themselves at risk.

“That was very dangerous, the way they shot there,” said Philip Stinson, a criminologist at Bowling Green State University in Ohio, after reviewing video of the shooting. “There are people, including officers, out there who are directly in the line of fire.”

Videos of the encounter show that a group of about seven officers had gathered in a semicircle around the woman, Pamela Cisneros, in a busy section of Midtown Manhattan. Gripping a knife in each hand, she begins windmilling her arms, and officers fire Tasers at her. Then she trots toward them, coming within a few feet of before some of the officers shoot at her.

As Ms. Cisneros is in the standoff facing the officers, Seventh Avenue remains open to a steady stream of traffic behind her, according to videos recorded from several different angles and posted on social media. Cars, taxis, cyclists and pedestrians can be seen going by seconds before the shooting begins, and a uniformed officer is standing in the street.

Stuart Schwartz, a retired New York Police Department captain who was assigned to the precinct that includes Times Square, also watched a video of the incident. “The officers — specifically, a supervisor or senior officer on the scene, as per the patrol guide and training — could have tried to close off the cross streets to make the scene safer,” he said.

“Thank goodness no civilian was killed,” he added, saying that the officers’ decision to stand in a semicircle was also dangerous.

“That means an officer could have shot a partner,” he said.

On Monday night, Police Commissioner Jessica S. Tisch said that the officers who confronted Ms. Cisneros “did exactly what they’re trained to do.”

They tried talking to Ms. Cisneros for four minutes, Ms. Tisch said, before opening fire after she refused their “numerous” commands to drop the knives.

While it may seem like four minutes would have been ample time for the police to close the street, Professor Stinson cautioned that it’s not that simple.

“They probably thought they’d be able to de-escalate the situation and take her into custody, as they do 999 times out of 1,000,” he said. Gunfire, he said, “was not where they thought it was going. It’s not until the very end that there’s that immediate danger.”

The mayor of New York, Zohran Mamdani, has said that more often, mental health workers should be sent to incidents when people are having mental breakdowns in public, and he has created an Office of Community Safety to overhaul the city’s policing of mentally ill people.

At the news conference with the police commissioner on Monday night, a reporter reminded Mr. Mamdani that he had “advocated before for mental health professionals to be at calls like this” and asked him whether that would have changed anything.

Mr. Mamdani replied that such a plan “would not be applicable when there is the threat of violence.”

“What we are speaking about is an alleged perpetrator who stabbed two individuals before being engaged by police,” he continued.

But Kirk Burkhalter, a retired New York police detective who is now a professor at New York Law School and teaches a course unit called “policing the mentally ill,” said that a mental health professional who brought a clinician’s expertise to defusing the situation might well have made a difference.

Given that the police talked to the woman for four minutes, that would have given the professional time to get to the scene, Professor Burkhalter said.

“In a perfect world, we should have enough mental health professionals to serve the entire city,” he said. “It’s a matter of having enough people and having them available, and being willing to invest the financial resources to have them available in the same way we staff precincts and firehouses.”

He added, “We’re just at the point where, given all these folks in mental distress in the city, we need to staff that so that they can respond.”