Many police departments have put in place training for officers in how to deal with mentally ill people, teaching them to defuse potentially volatile situations and to treat people who suffer from psychiatric illnesses with respect. But officers can sometimes make a crisis worse, either out of fear or in a reflexive effort to control the situation and enforce compliance.

Although no agency or organization tracks the number of police shootings nationally that involve people with mental illnesses, a report by the Treatment Advocacy Center and the National Sheriff’s Association, based on informal studies and accounts, estimated that half the number of people shot and killed by the police have mental health problems.

That number is higher in Albuquerque, where since 2010, 37 people have been shot by the police, 23 of them fatally. According to a report by the New Mexico Public Defender Department, which offers free legal services to indigent clients, nearly 75 percent of those shot in 2010 and 2011 suffered from mental illness. In one case, in July 2010, police officers responding to a domestic violence call shot a man suffering from schizophrenia who had threatened them with a knife. In April 2011, another schizophrenic man was killed in a scuffle with plainclothes detectives, who had entered his home to serve a warrant.

The Justice Department has been investigating whether the Albuquerque Police Department has a pattern and practice of using excessive force. In its guidelines for dealing with mentally ill people, the department includes examples of delusional statements — like “Everyone is out to get me” — and the potential risks posed by ill people, like a loss of emotional control. The guidelines also tell officers to “move slowly, being careful not to excite the subject” and to “provide reassurance that the police are there to help.”

Like an increasing number of police departments across the country, Albuquerque’s uses a crisis intervention team model, in which specially trained officers are dispatched to a scene when a mentally ill person is involved. Currently, about 25 percent of officers in the department are certified for the crisis teams.

Shaun Willoughby, vice president of the Albuquerque Police Officers Association, said the Police Department got its first crisis intervention teams in the 1990s and had since made de-escalation techniques part of the training for recruits as well as officers. But the reality on the street is more complicated.