NEW YORK >> A year before a police sergeant shot and killed a bat-wielding woman with schizophrenia, the New York Police Department began giving officers specialized training on how to handle the mentally ill.

But the sergeant, who was charged this week with murder, hadn’t received it. The October shooting of Deborah Danner became a searing illustration of the argument for the training, which so far has reached about 5,800 of the department’s 35,000 officers. The NYPD says it’s trying to extend it as widely and quickly as possible.

Mental health advocates and a city police watchdog group have praised the program, but they also have said it needs to be better put into practice.

“The training of police officers is critically important,” says Steven Coe, CEO of Community Access, a mental health advocacy and services organization. But “there’s things the city needs to be doing, overall, beyond the training.”

While the NYPD already had a small, highly trained unit for mental health cases, the crisis intervention training was meant to give more officers a better chance at de-escalating confrontations.

It’s now being expanded to additional shifts. Since Danner’s death, the department has been focusing on training sergeants and other higher-ranking officers.

Police spokesman Stephen Davis said the aim is to prepare as many officers as possible, but it takes time.

“We’re moving in the right direction,” he said. “It’s a priority.”

The NYPD responded to 157,000 calls of people in crisis last year.

Most end without harm. But not the call that brought Sgt. Hugh Barry to Danner’s apartment on Oct. 18, 2016.

Barry persuaded the 66-year-old Danner to drop a pair of scissors, police said. But after she picked up a baseball bat and brandished it toward him, he shot her twice in the torso, prosecutors said. Danner was black and Barry is white.

Barry had a stun gun but didn’t use it, and prosecutors said he disregarded the training he did have.

The eight-year police veteran has pleaded not guilty. His union leader decried the charges, saying it’s clear the sergeant didn’t intend to harm Danner and had to make a split-second decision.

Crisis intervention training explores how to recognize signs of mental illness, respond to such calls and empathize with someone in the throes of a crisis. During the four-day program, officers hear from patients, mental health professionals and police officials.

Mental health advocates — and a January report from the city’s inspector general for police — say the training is well-done, but not so well deployed.

“If you’re going to have people trained, you have to follow through,” said Jay Ruderman of the Ruderman Family Foundation, a Boston-based charity that aids and advocates for people with disabilities. “They did all the right things, except for the implementation.”

The city’s 911 dispatchers can’t tell which officers have had the training, so they can’t steer them to calls of people in crisis. The NYPD notes, however, that police supervisors have a list of trained officers and can direct them as needed.

The department also has said it needs other city agencies to do their part by creating drop-off centers where officers can take people who don’t need to be arrested or hospitalized. A 2014 city plan pledged to open two such centers by 2016, but it hit snags. Democratic Mayor Bill de Blasio recently said they’re expected to open next year.

Meanwhile, the murder case surrounding Danner’s death will play out in court.

In a 2012 essay, she agonized over the deaths of mentally ill people like her at the hands of police.

At the top of her “wish list” for helping people like herself: “Teaching law enforcement here how to deal with the mentally ill in crisis.”