SAN ANTONIO — The San Antonio police’s strategy for responding to calls involving people who are mentally ill is being hailed as a national model amid rising anger over police brutality toward and high incarceration rates of people with mental health issues.

The approach was used in mid-March when sheriff’s deputies responded to a call in eastern San Antonio when a woman called because her son, who had refused to take his medication, was aggressive and threatening. She said he was mentally ill, hadn’t bathed or eaten and was paranoid.

The deputies from the Bexar County Sheriff’s Office alerted the office’s mental health unit, which sent officers who specialize in mental health to speak to the man calmly, with the goal of de-escalating the situation, according to Sgt. Raul Garza, the supervisor of the unit.

They maintained a patient, unhurried demeanor, and the man agreed to go with the deputies to a treatment facility.

Garza said deputies in the mental health unit have used force only twice since 2012.

On March 9 a police response to an incident just outside Atlanta involving a mentally ill person turned out very differently. A DeKalb County officer arrived at an apartment complex where a nude man was crawling around, knocking on doors and causing a disturbance, according to police. Officers said the man, Anthony Hill, 27, rushed at the officer, who shot and killed him. Hill was unarmed. The officer who shot him was placed on administrative leave, and the Georgia Bureau of Investigation is looking into the shooting.

Nationwide, half the people shot and killed by police have mental health problems, according to a 2013 estimate by the Treatment Advocacy Center and the National Sheriffs’ Association.

Advocates say not only does the San Antonio and surrounding Bexar County program reduce violence, but it also keeps the mentally ill out of lockup.

In 44 states, more people with mental illness are in jail or prison than are in state mental hospitals, according to the Treatment Advocacy Center. Approximately 20 percent of jail inmates and 15 percent of state prison inmates have a serious mental illness, according to the organization.

In San Antonio about 2,300 people a month are referred to treatment who likely would have been incarcerated were it not for the program, said Leon Evans, the president and CEO of the county mental health agency, the Center for Health Care Services.

The program, which was rolled out in 2003, involves police, sheriff’s deputies, jail, courts, hospitals and county mental health facilities and has received a Gold Achievement Award from the American Psychiatric Association.

All police receive special training and have access to a mental health unit for assistance, a 24-hour crisis center provides assessment and referrals, the jail and courts screen for mental illness and can shift inmates into treatment, and the county mental health agency has created a variety of treatment options.

“Police have become front-line mental health providers,” said Jerry Murphy, the director of the law enforcement program at the New York–based nonprofit Council of State Governments Justice Center.

Across the country, jails and prisons house hundreds of thousands of mentally ill inmates. Many of them have little access to treatment and are subjected to abuse by other inmates and isolation, according to Christine Sarteschi, an assistant professor of social work and criminology at Chatham University in Pittsburgh.

Mentally ill inmates have difficulty complying with jail and prison rules and are seen as disruptive, according to a Human Rights Watch report to Congress in 2009. A higher percentage of them are put in solitary confinement, compared with the general population. According to the National Alliance on Mental Illness (NAMI), 80,000 inmates — not just mentally ill prisoners — are in some form of solitary confinement in U.S. jails and prisons every day.

San Antonio’s county jail was severely overcrowded in 2002. As a result of the diversion program, it now has more than 800 free beds, according to Evans. He estimated the city and county save $11 million to $12 million a year as a result.

The first step toward change in San Antonio was to improve police training.

The city turned to crisis intervention training, developed for police in Memphis, Tennessee, and used by many other police departments. The San Antonio branch of the NAMI worked closely with the city’s police, providing mentally ill people and their families as well as mental health professionals to talk to police.

“They share their stories” of living with mental illness and their experiences with police, said Liza Jensen, the executive director of NAMI San Antonio.

Police learn to determine whether they’re dealing with someone who likely has a mental health diagnosis, she said. When signs of psychiatric distress are apparent, they’re taught to function more like a social worker than a law enforcement officer.

Officer Ernie Stevens recalled being dragged to training about eight years ago.

A woman whose son had schizophrenia spoke to the class, saying her son got angry and aggressive whenever he saw police. Stevens remembered her saying, “I know that one day, one of you officers will have to come to my house and shoot and kill my son.”

“That’s not right,” Stevens thought.

Today he is deeply committed to his work in the police mental health unit, which includes five officers, a supervisor and four psychologists. He responds to mental-health-related calls and provides backup and specialized help for patrol officers.

Recently he sat on the floor in an apartment talking calmly to a 12-year-old girl whose friend had called 911, afraid that the girl might be suicidal. With her consent, he phoned her mother, and the three talked about places she could get help.

A mental health unit exists in the sheriff’s office also and includes deputies and mental health professionals. Patrol officers call the unit when they believe they’re dealing with a mentally ill person.

Active listening is the key when dealing people who appear to be mentally ill, Stevens said. “We help them de-escalate,” he said. “We sit and build rapport.”

Developing this expertise is a challenge for police departments, said Murphy. “It requires a different skill set than is usually used by police,” he said.

All San Antonio–area law enforcement officers get 40 hours of training, which has been extended to paramedics, firefighters and school, airport and hospital security officers, Jensen said.

However, training “does not solve the problem if there aren’t alternatives to jail,” Murphy said.

The county built a clinic in 2008, the Crisis Care Center, which includes a detox area. The 16-bed center operates 24/7 and provides mental health assessments and referrals to treatment when police bring someone in. Rather than go to an emergency room and wait for hours, police can get in and out of the Crisis Care Center quickly. Mental health personnel work closely with courts to screen people after arrest.

The program also brings many community services together to deal with multiple problems that lead mentally ill people to jail — including homelessness and substance abuse.

Roughly 30 percent of chronically homeless people are mentally ill, according to the U.S. Substance Abuse and Mental Health Administration. About half the chronically homeless have substance abuse problems, and many end up being arrested.

In 2010 the Bexar County mental health agency opened a campus, Haven for Hope. It has homeless shelters for men and women, a drug and alcohol recovery program and day treatment for mental illnesses. Homeless people who don’t want to use those services can sleep in a large outdoor courtyard and use the showers and laundry facilities. Approximately 500 to 600 people sleep in the courtyard each night.

The number of homeless people on the streets downtown has dropped 70 percent, according to Evans.

San Antonio is not the only city to take a new approach to mentally ill offenders. Los Angeles, for example, has a triage desk staffed by police and mental health professionals at police headquarters and in four police bureaus. Patrol officers can call the desk for guidance.

Houston; Salt Lake City; Madison, Wisconsin; and Portland, Maine, have also created diversion programs, according to Murphy. But only about 12 percent of the 18,000 police departments nationwide provide mental health training, he said.

“It’s a long, long way to go before we train all police to respond to mental health calls and de-escalate the crisis,” he said.

San Antonio has not solved all its problems. Some police are still taking the mentally ill to emergency rooms, bypassing the crisis center, according to Jensen.

And outside of its mental health program, there is evidence the department may not be a model of good policing.

“We’ve received complaints of excessive use of force,” said Wayne Krauss Yang, an attorney with the nonprofit Texas Civil Rights Project. Complaints include unjustifiable forced entry into houses and unwarranted “grabbing, pulling and beating” of people in public, he said.

A 2011 report by the Civil Rights Project asserted a pattern of misconduct, including illegal searches and sexual offenses.

The San Antonio police department did not respond to a request for comment on the reports by deadline.

“We would like to see [police] put into place more policies and training to prevent this,” he said.

Anna Simonton contributed to this article.