PHOENIX — Maricopa County has made changes to how it deals with the homeless in its jail system, helping them find places to live, health care and employment with the goal of saving money and cutting down on arrests.

Homeless inmates began meeting with caseworkers in jail last month to connect them to apartments, medical care and jobs immediately upon release in an effort to keep them from coming back.

The “Hand in Hand” initiative grew out of an experiment with jail intake forms. Curious Correctional Health staffers added a checkbox asking inmates whether they had gone without housing at any point in the last year, The Arizona Republic reported (http://bit.ly/2uVFGbD ).

Officials were shocked by the result: One in four inmates said yes. The rate was even higher for people with mental illness.

“I was blown away,” said Dr. Dawn Noggle, mental-health services director for the county’s Correctional Health Services Department. “I knew that it was high, but … now we’re able to quantify the connection between incarceration, serious mental illness and homelessness. It’s unmistakable.”

Diving deeper into the data, staffers discovered nearly every chronic repeat offender had been homeless.

Those 59 people, who combined were arrested more than 1,000 times over two years, were costing taxpayers thousands. Some had racked up booking and jail-housing expenses of $30,000 or more each, even though most charges were misdemeanors such as drinking in public, littering, shoplifting or failing to show up for court.

To make the program work, the Maricopa County Housing Authority has agreed to earmark apartments, and the county Human Services Department has dedicated about $350,000 in federal funding to the program.

Two nonprofits, Community Bridges Inc. and Native American Connections, will pair homeless inmates with caseworkers who can identify their needs before they get out. After release, the inmates will receive a year of assistance with job placement, conflict resolution and other life skills.

The first candidates for housing will be chosen from a seven-week jailhouse substance-abuse program called Mosaic that teaches emotional coping and employment skills, and has received national recognition, Noggle said. Eventually, she hopes to expand the housing program to all homeless inmates.