A 66-year-old schizophrenic woman who was fatally shot by a police sergeant at her Bronx home might still be alive if a cop specially trained to deal with the mentally ill had been dispatched instead, according to a newly released report critical of the NYPD.

The finding was part of an 18-month investigation by the Inspector General for the NYPD that concluded nearly 5,000 officers trained to deal with the mentally ill are not dispatched properly.

The report was released Thursday by the city’s Department of Investigation, which oversees IG Philip Eure’s office.

Neighbors of the slain Bronx woman, Deborah Danner, called 911 on Oct. 19, reporting that she was acting erratically. When cops arrived, she threatened them with a pair of scissors, and then a baseball bat. The sergeant shot her twice after she swung at him, officials have said.

The shooting prompted Police Commissioner James O’Neill to call out his own department. “We failed,” he said the following morning.

Eure suggests officers trained as part of the NYPD’s Crisis Intervention Team (CIT) should have been dispatched to the home. But the program is plagued by a lack of central control and an inability to dispatch officers where they are needed, the report found.

The investigation’s most notable finding was the “NYPD’s failure to fully integrate and use this training within the totality of NYPD’s everyday policing,” according to the report.

The NYPD began providing officers with CIT training in June 2015. As of December 2016, about 4,700 cops were trained. That’s about 21 percent of the department’s patrol officers.

But the NYPD hasn’t created a way to have the officers dispatched to calls when they are needed. Emergency dispatchers have no way of knowing where the trained officers are when they get a call about someone in “mental crisis,” according to the report.

“NYPD has developed a strong CIT training, and we encourage NYPD to carry that initiative further and expand its training into a comprehensive CIT program to improve results for officers and the public alike,” Eure said in the report.

“In particular, the Department needs to begin to actually assign CIT-trained officers to mental crisis incidents and create a real timeline for doing so.”

NYPD Assistant Commissioner for Communication and Public Information J. Peter Donald said the NYPD was “currently assessing the on-going CIT program in an effort to more effectively address the availability of trained personnel to respond to calls for the emotionally disturbed, in the most timely and efficient manner possible.”

He said the NYPD is providing “a list of all crisis intervention trained officers to supervisors in commands during every shift …”