The push to saturate New York City’s subway with police officers last year was supposed to make the system feel safer after a sequence of shocking crimes rattled commuters and discouraged many from using public transit.

Months later, officials say the surge in police presence has yielded some favorable results: Ridership is rising and major crimes are dropping since the initiative intensified in October.

But after a passenger choked a homeless man to death on the subway last week, a familiar debate has emerged over whether more police officers are the solution to subway violence, especially when they confront people who are mentally ill.

The homeless man, Jordan Neely, 30, was shouting at riders in a train car when another man, Daniel Penny, 24, placed him in a chokehold and killed him. The killing has stirred outrage and divided city leaders and the public. Mayor Eric Adams has since been criticized not just for his reaction to Mr. Neely’s death, but also for the aggressiveness with which he has deployed law enforcement and targeted homeless people in the subway.

In addition to the political debate over using the police to help with societal problems like mental illness and homelessness, there is the question of whether the mayor’s strategy is working, especially in a vast and dynamic system that officers cannot possibly monitor in its entirety.

Have the mayor’s efforts reduced crime and made New Yorkers feel safer, as Mr. Adams and his supporters argue? Or have they heightened fears and even endangered homeless people by reinforcing riders’ anxieties about mentally ill people, as some of his critics have said — setting the stage for encounters like the one between Mr. Neely and Mr. Penny? On Wednesday, Mr. Adams said in a speech, partly in response to those criticisms, that while he didn’t control the legal process, “one thing we can say for sure: Jordan Neely did not deserve to die.”

Like other large American cities, New York City has had to contend with a confluence of problems exacerbated by the pandemic, including rises in housing prices and homelessness, in unemployment and crime, and in mental health issues, and intensifying political debates over how to solve them.

After Mr. Adams took office, he announced plans to deploy a wave of police officers across the system. That same month, many subway users were disturbed by the death of Michelle Go, who was shoved in front of an R train by a homeless man who the police said had a history of crime and mental illness.

In October, after a continued rise in violence in the subway, the state said it would help the city pay for an additional 1,200 overtime shifts per day for police officers to watch over the system.

“We can tell New Yorkers all the time that we have decreased crimes in certain areas, but if New Yorkers don’t feel safe, we are failing,” Mr. Adams said at the time, adding, “That’s why the omnipresence of police officers and the removal of those who are dealing with mental health issues is crucial to our second phase of this important plan.”

In recent months, officers on the subways have detained significantly more people for breaking the law. Police statistics show there were about 3,000 arrests in the transit system from January through March of this year, compared with 2,000 arrests during the same period in 2022.

A Police Department representative said that transit officers had conducted about 515,000 train and subway inspections so far this year, putting them on track to exceed the roughly 750,000 inspections conducted during the first 10 months of last year.

“The N.Y.P.D. constantly evaluates emerging crime trends and redeploys personnel based on the trends observed,” the representative said, noting that “the added numbers of station inspections and train runs create an omnipresence that riders, at all hours, can see and feel as they make their way to school, work, or home”

Even after the rate of crime increased during the pandemic, the chances that someone might be a victim of a violent crime while riding the subway remained incredibly remote, according to a New York Times analysis of M.T.A. and police statistics.

So far this year, major felony crimes have decreased compared with the same time period last year, though it is too soon to know for certain whether that dip is statistically significant.

There were 10 murders in the system in 2022, compared with an average of two per year in the five years before the pandemic began. In 2023, the most recently available statistics show that there has been one murder through March.

Most of the roughly 10,000 calls for aid in the transit system that the police have responded to this year have been about homeless people in need of help, according to a Police Department spokesman. The majority of people in those cases accepted the support and agreed to go to a homeless shelter. Another 1,200 needed medical care and were taken to a hospital.

The Police Department did not respond to questions about how many officers, on average, work in the system on a given day, or how many arrests or outreach efforts involved homeless or mentally ill people and how those numbers compared with years past.

Since Mr. Adams announced his first push early last year to remove homeless people from the subway system, roughly 4,600 New Yorkers experiencing homelessness in the transit system have checked in to a shelter, according to city officials. As of this week, about 1,300 of them remained in shelters.

The effort has also been criticized for violating the rights of homeless people, especially after the mayor urged police officers and other responders last year to take people with severe untreated mental illnesses to hospitals, against their will if necessary.

Encounters between the police and severely mentally ill people can end in tragedy when officers are not well suited to deal with someone behaving erratically, in part because people in a state of psychosis often cannot follow commands. That is why many advocates, experts and elected officials have urged the city to focus instead on solutions that are meant to help people cope with mental illness before they reach a crisis.

“The mayor’s insistence on controlling those in need, instead of taking on the city’s housing crisis or lack of access to health care only fuels stigma against homeless New Yorkers and those living with mental illness,” Donna Lieberman, the executive director for the New York Civil Liberties Union, said in a statement. “Arrest and forced hospitalization do nothing to address the root drivers of homelessness or the chronic lack of access to mental health care.”

On Wednesday, the mayor gave a speech addressing Mr. Neely’s death, saying that he had called for reforms in the way mental illness is addressed “from the very beginning of this administration.”

The mayor has pushed forward a number of other initiatives to help mentally ill New Yorkers that do not involve the police, including programs to connect people to community-based treatment and to send mental health professionals and paramedics in response to 911 calls that involve people in mental distress.

The city is also expanding the number of “intensive mobile treatment” teams that respond to people with mental illness or substance abuse issues living in shelters, streets and subways and that offer them a range of services. The teams typically do not coerce clients to accept care or shelter, but spend weeks and often months trying to connect them with help. They will soon serve nearly 1,000 New Yorkers with some of the greatest needs.

And last October, the state said it would set up two new units at psychiatric centers, including 50 inpatient beds, to take in people with serious mental illnesses.

After Mr. Neely’s killing, many New Yorkers have called for more investments like these to help some of the city’s most vulnerable people, rather than more law enforcement.

“We understand our current times have created a heightened sense of fear (sometimes reasonable, sometimes not),” Lennon Edwards and Donte Mills, lawyers for Mr. Neely’s family, said in a statement last week.

But, they said, “Passengers are not supposed to die on the floor of our subways.”

Hurubie Meko and Maria Cramer contributed reporting.