They called her the “million dollar woman.” Los Angeles 911 dispatchers heard from her on a daily basis – sometimes multiple times.

The complaint was always the same: The caller said she couldn’t breathe. Each time, emergency crews packed her into an ambulance. And each time, unable to find any medical problem, emergency room doctors released her without treatment.

Those ER visits cost the city more than $1 million in a single year – and did little to assist the woman, says Lt. Lionel Garcia, longtime director of the L.A. Police Department’s Mental Evaluation Unit (MEU).

It wasn’t until mental health clinicians working directly with the LAPD got involved that the root causes of the woman’s distress became clear: She was lonely and experiencing delusions. Once she was connected with supportive services, the 911 calls ceased.

The department’s unusual partnership with the Los Angeles County Department of Mental Health has become a nationally recognized model for police departments.

L.A. isn’t the only city to co-deploy officer-clinician teams, but it is the biggest and most robust program in the United States. In 2010, it was designated a national training site, and officers from as far away as Australia have reached out to Lieutenant Garcia.

By partnering beat cops with mental health clinicians, the MEU reined in costs associated with frivolous 911 calls. It also connected thousands of individuals with counseling and support, reducing incidences of force used on individuals with mental illness and alleviating the burden on overcrowded emergency rooms and the criminal justice system.

Diverting nonviolent offenders to mental health services is ultimately better for their recovery and saves taxpayers money, says Fred Osher, director of health systems and services policy at The Council of State Governments (CSG).

“To be treated within a mental health climate and environment, as opposed to being in custody within a jail setting, has enormous implications for one’s recovery and the cost of one’s recovery,” Dr. Osher says.

In recent years, US jails and prisons have become the nation’s de facto mental hospitals, advocates say. There are 10 times as many inmates diagnosed with severe mental illness in the penal system as patients in state mental institutes, the nonprofit Treatment Advocacy Center estimates. Just under half of those inmates are incarcerated for nonviolent offenses, according to the National Alliance on Mental Illness.

“We have essentially criminalized mental illness,” Sen. Al Franken (D) of Minnesota said during a kickoff event for Stepping Up, an initiative to reduce the number of people with mental illness in jails. “Instead of providing people with adequate access to mental health treatment, we let them fall through the cracks and languish in jail.”

Studies have shown that mentally ill inmates cost more to incarcerate and spend more time in jail than other inmates.

About 12 percent of the nation’s 18,000 law enforcement agencies use crisis intervention training to help officers respond compassionately to individuals in the throes of mental distress, Osher says. But in the end, officers are left with just two choices: arrest them or send them to the emergency room.

“That doesn’t cut it,” says Garcia. “There are significant shortcomings when you have just one single-layered approach.”

The LAPD deploys doctors, nurses, and social workers alongside patrol officers. At any given time, there are four or five officer-clinician teams patrolling together. For officers responding on their own, clinicians staffing a MEU triage desk are available 24 hours a day to consult.

And case assessment managers follow up with individuals to make sure they are receiving the correct services.

To be sure, the LAPD has not been without controversy in its handling of individuals with mental illness. Last week, the Los Angeles police commission ruled that an officer's use of deadly force last August against Ezell Ford, a mentally ill man, violated LAPD policy. And last month Samuel Arrington, a mentally ill homeless man, filed a federal civil rights lawsuit against 14 LAPD officers over his arrest last summer, saying excessive force was used.

Still, other cities have set up programs similar to the MEU in Los Angeles. Boston, for one, has a fledgling program on a smaller scale. Ben Linsky, a counselor who has been with the unit since its inception in 2011, says he struggled to gain acceptance when he first arrived. 

“At first, turf issues were horrendous,” Mr. Linsky says. “It took a really long time to be accepted by rank and file.”

Linsky is one of two clinicians assigned to the Boston Police Department. Together they cover some of the poorest areas of the city, but whole swaths of Boston are left uncovered. Linsky has asked Garcia for help in scaling up Boston's program.

Officers on the force have come to see Linsky as an asset, says Officer Jason Romano, who has been riding with Linsky for about a year.

“I think it’s really beneficial for someone who’s not in the right frame of mind to have someone who can go in and say, ‘I’m not a police officer. Let me help you,' " Mr. Romano said during a ride-along last month. "That’s an invaluable tool."