CHICAGO — Peering through the chain link of a holding pen at the Cook County Jail, a man wrapped in a navy varsity jacket leans toward clinical social worker Elli Petacque Montgomery, his bulging eyes a clue that something’s not right.

“They say I got bipolar, that’s all,” he said.

“OK, are you taking your meds?” she asks.

“When I can get them,” he answers.

“I’m down here every day,” Montgomery said. “Every morning I hear this.”

The Chicago jail and many of its 3,300 counterparts across the country have become treatment centers of last resort for people with serious mental illnesses, most arrested for non-violent crimes. And like other jails, it is awash in a tide of booking and releases that make it particularly unsuited for the task.

U.S. jails, most of whose 731,000 inmates are trying to make bail or awaiting trial, hold roughly half the number in prisons. But last year, jails booked in 11.7 million people — 19 times the number of new prison inmates. The revolving door complicates the task of screening for mental illness, managing medications, providing care and ensuring inmate safety.

“Jails are churning people,” said Henry J. Steadman, a consultant to government agencies on how courts and correctional facilities deal with people with mental illnesses.

Experts have pointed to rising numbers of inmates with mental illnesses since the 1970s, after states began closing psychiatric hospitals without following through on promises to create and sustain comprehensive community treatment programs.

But as the number of those with serious mental illnesses surpasses 20 percent in some jails, many have struggled to keep up, sometimes putting inmates in jeopardy.

The Associated Press has reported that at least nine of the 11 suicides in New York City jails over the past five years came after operators failed to follow safeguards designed to prevent self-harm by inmates. The AP’s investigation into the deaths of two mentally ill inmates at the city’s Rikers Island complex — one who essentially baked to death in a 101-degree cell in February and the other who sexually mutilated himself last fall — have prompted promises of reform.

Federal law protects the rights of people in jails and other institutions. But in temporary holding facilities, dealing with serious, long-term mental illnesses requires operators to rethink what they do, Cook County Sheriff Thomas J. Dart said.

“You’re given a court order by a judge to hold this person in the jail until you’re told not to,” Dart said. “You’re not supposed to do anything other than feed him, give them a bed, make sure they don’t harm anyone else or themselves. … You’re not in there trying to cure people.”

Many jails are dealing with similar dynamics, with sometimes disturbing results.

—In June, federal officials cited “deplorable” conditions for mentally ill inmates in the Los Angeles County jails as partly to blame for 15 suicides in 30 months. The L.A. system, the country’s largest with 19,000 inmates, has been under federal supervision since 2002, but still fails to adequately supervise inmates “with clearly demonstrated needs,” the Justice Department concluded.

—In Pensacola, Florida, Justice officials last year issued a scathing report about conditions at the Escambia County Jail. Records showed many inmates who requested care were never seen by a mental health professional. When inmates refused to take medications, the jail merely removed them from its list of those with a mental illness.

—In Columbus, Nebraska — seat of a county of 33,000 — six Platte County Detention Center inmates attempted suicide early this year, as many as in the previous 10 years combined. Jon Zavadil, the recently retired sheriff, said about 80 percent of all inmates medicated for some type of mental illness.