The week before Labor Day was overshadowed by violence at two famous sites in New York City that left a young mother dead and two people fatally shot by the police.

On Monday, a woman stabbed two people, one fatally, in Times Square before she was shot dead by the police. On Friday, a man armed with a knife who scaled the cables of the Brooklyn Bridge claimed he had a bomb and threatened to kill himself. When officers tried to talk him down, the man raised the knife, and an officer shot him.

The killings, both of which involved people in mental distress, appeared to be justified according to the Police Department’s rules that govern when officers can use deadly force, law enforcement experts said. The episodes are under internal and state investigation, a standard procedure when someone dies in an encounter with the police.

Mayor Zohran Mamdani pledged during his campaign to have mental health professionals, rather than the police, respond to certain emergencies. As mayor, he created an Office of Community Safety in March to overhaul the city’s policing of mentally ill people.

Yet the shootings last week show how challenging it would be to involve those professionals in dangerous, fast-moving events in which armed individuals experience a mental health crisis.

Last week’s deaths were the eighth and ninth fatal police shootings in New York City in 2026, according to the state attorney general’s office. In 2024, the latest year for which police data was immediately available, 14 people were killed in police shootings, up from seven people in 2023 and 13 people in 2022.

The mayor’s response

Mr. Mamdani supported how the police acted in the two episodes, as did his police commissioner, Jessica S. Tisch. After Pamela Cisneros, 49, fatally stabbed Erin Piacenti, 32, on her first day back at work after maternity leave, and stabbed Tak Kam, 68, who was visiting with his wife from Rhode Island — Mr. Mamdani praised the police officers “who stepped in and prevented a horrific attack from becoming even worse.” He added that his own plan to have social workers respond to 911 calls “would not be applicable when there is the threat of violence.”

Four days later, on Friday, Mr. Mamdani said that the officers on the Brooklyn Bridge had tried to de-escalate the situation for around an hour, and that they had urged the man, Chaun Bottom, 41, not to jump. He added that, “The man was holding a knife and threatened the officers.”

Videos appear to support officers’ actions

Policing experts who watched videos of the shootings said it appeared that the officers were justified in firing their guns. In both cases, the police were approached by a person wielding a weapon, even after they tried to de-escalate the situation.

“It’s an emergency-type situation where they have to take immediate action,” said Kenneth Quick, a former inspector in the Police Department who now teaches at DeSales University in Pennsylvania. “There’s not much they can do in that moment other than what they did.”

Still, the shooting of Ms. Cisneros has led to some scrutiny. Several law enforcement experts have questioned whether the police did enough to assess the risk to pedestrians in bustling Times Square.

“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.”

Ms. Tisch said that the officers who confronted Ms. Cisneros had tried to get Ms. Cisneros to drop her weapons for four minutes, but that she had refused their commands. The officers “did exactly what they’re trained to do,” Ms. Tisch said.

Mario Cisneros, 78, the father of Ms. Cisneros, did not blame the police for his daughter’s death. “She acted like an animal,” he said in Spanish in an interview last week.

In Mr. Bottom’s case, Mr. Quick said it appeared that the officers had been trying to get closer to offer emergency mental health assistance. By the time Mr. Bottom began coming down the cable with a knife, the officers were already harnessed to the cables themselves and unable to retreat, he said.

Mr. Bottom’s mother and brother have said they are skeptical of the Police Department’s description of the events. In an interview on Friday, Mr. Bottom’s brother, Jonathan Craine, said he watched a video of the interaction in which Mr. Bottom appeared to retreat from the officers.

“It doesn’t make sense,” he said of the officers’ decision to fire.

When could mental health workers help?

Armed individuals in the throes of a mental health crisis can jeopardize the safety of those around them, including social workers. The Mamdani administration is focused on providing mental health assistance before situations escalate into violent incidents like the ones last week, Sam Raskin, a spokesman for the mayor, said on Saturday.

“The Mamdani administration believes preventing tragedy begins with investing in support before someone reaches a point of acute distress,” he said.

Dana Rachlin, a founder of We Build the Block, a public safety group based in Brooklyn, said that she supported the mayor’s plan to use mental health workers for early intervention, adding that a more effective mental health system was essential to preventing shootings.

“There’s a million things that happen before that moment of police meeting that person,” Ms. Rachlin said. “We have to cultivate the environment for these things to work.”

Officers would also prefer an early-intervention model, Mr. Quick said. But the episodes that unfolded last week were “already way too far gone, and into too dangerous waters for them to have any other kind of approach.”

How do authorities investigate shootings that involve the police?

The Police Department’s Force Investigation Division must examine all cases — including the two from last week — in which an officer discharges a firearm, or when they involve serious injury or death at the hands of the police. Such inquiries are routine, signifying the next step in the department’s adjudication process.

The New York attorney general’s Office of Special Investigation is also required to investigate every reported instance in which a police or a peace officer causes a death. These investigations themselves do not indicate any wrongdoing, though there have been cases in which they led to criminal charges against officers.