ALBUQUERQUE, N.M. » James Boyd, a homeless man camping in the Sandia Foothills here, could hear the commands of the police officers who were trying to move him out.

The problem was that Boyd, 38, had a history of mental illness, and so was living in a different reality, one in which he was a federal agent and not someone to be bossed around.

"Don’t attempt to give me, the Department of Defense, another directive," he told the officers. A short while later, the police shot and killed him, saying he had pulled out two knives and threatened their lives.

The March 16 shooting, captured in a video taken with an officer’s helmet camera and released by the Albuquerque Police Department, has stirred protests and some violence in Albuquerque and prompted the FBI to begin an inquiry into the death. But it has also focused attention on the growing number of people with severe mental disorders who, in the absence of adequate mental health services, are coming in contact with the criminal justice system, sometimes with deadly consequences.

In towns and cities across the U.S., police officers find themselves playing dual roles as law enforcers and psychiatric social workers. County jails and state prisons have become de facto mental institutions; in New York, for instance, a surge of stabbings, beatings and other violence at Rikers Island has been attributed in part to an influx of mentally ill inmates, who respond erratically to discipline and are vulnerable targets for other prisoners. "Frequent fliers," as mentally ill inmates who have repeated arrests are known in law enforcement circles, cycle from jail cells to halfway houses to the streets and back.

The problem has gotten worse in recent years, according to mental health and criminal justice experts, as state and local governments have cut back on mental health services for financial reasons. And with the ubiquity of video cameras both in ordinary citizens’ hands and on police officer’s helmets and in cruisers the public can more readily see what is going on and respond.

"I think that this issue hits every city, every part of the country where you have people who are walking on the street who normally would have been under some kind of treatment or institutionalized," said Chuck Wexler, executive director of the Police Executive Research Forum, a Washington-based nonprofit that in 2012 released a report calling for minimizing the use of force by the police in situations involving mental illness.

Dr. E. Fuller Torrey, a psychiatrist and the founder of the Treatment Advocacy Center, a nonprofit group in Arlington, Va., that promotes access to mental health care, said police officers had by default become "the first line of contact" for severely troubled people who once might have gone to a community clinic or mental health crisis center.

Torrey pointed to San Diego, where calls to the sheriff’s office involving mentally ill people nearly doubled from 2009 to 2011, and to Medford, Ore., where, he said, the police in 2011 reported "an alarming spike in the number of mentally ill people coming in contact with the police on an almost daily basis."

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 the mentally ill, 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.

"Our reactions are based on the actions of people," Willoughby said, setting up a dynamic that often leaves the officer no alternative but to use "a strong hand."

The department does not pair officers with mental health workers, as some cities do. The Los Angeles Police Department’s specialized mental evaluation unit, for example, has a staff of 60, with 30 mental health clinicians, according to Detective Charles Dempsey.

The New York Police Department has not adopted the crisis intervention team model, which was developed by the Memphis, Tenn., Police Department, but has opted instead for its own protocols and training for handling mentally ill people, who are known as emotionally disturbed persons, or EDPs in the department’s jargon.

All officers in New York receive basic training for handling such calls, said Stephen Davis, the police department’s top spokesman, but the rule is to bring in the Emergency Service Unit, whose officers have specialized training in this and other areas. The unit also tracks mentally ill people who have had contact with the police over time, trying to make sure they receive appropriate treatment.

People with mental illness are often approached by police officers for minor crimes like disorderly conduct or trespassing. Boyd, whom the Albuquerque police said had a history of violence and who appeared to be turning away from the officers when he was shot, attracted law enforcement attention for camping illegally.

About 6 percent of the population, or one in 17 Americans, suffer from a serious mental illness, according to the National Institute of Mental Health. Studies suggest that the mentally ill are involved in only about 4 percent of violent crimes. But when untreated, severe mental illness is associated with higher rate of violence, researchers have found.

The lack of adequate mental health services for the severely ill, which began during the years of deinstitutionalization in the 1960s and has worsened in the ensuing decades, increases the chance of a crisis escalating into violence.

"It’s like if we stopped treating heart disease until people had heart attacks," said Ronald S. Honberg, director of policy and legal affairs at the National Alliance on Mental Illness. "We’d be seeing lots of people having heart attacks in the street. That’s what’s happened in our mental health system. Once people get to the point of crisis, that’s a difficult time to start treatment."

Willoughby, for his part, said that for Albuquerque officers, "More training is a great thing, but to say you’re going to train this problem away is ridiculous." He said that people with mental illness tended to go "through the revolving door of jails" without getting the help they need, then go back on the streets "to be dealt with by the police time and time again, which only contributes to the problem."

The mayor of Albuquerque, Richard J. Berry, defended the police force, saying in an interview on Monday that during a demonstration on Sunday, "I saw the department act with professionalism and restraint throughout the day."

But the police officers get little sympathy from people whose lives have been touched by the shootings.

"They don’t seem to learn from their past mistakes, and that troubles me," said Stephen Torres, the father of the man who was killed by plainclothes officers in April 2011.

The Albuquerque police have "very well-drafted, very well-thought-out" procedures on dealing with mentally ill individuals, but he believes, "the officers don’t follow them, and they don’t get disciplined" for not following them, he said.

"If they did," said Torres, a family lawyer, "my son would still be alive."

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