The sun rises behind the Golden Gate Bridge. (Marcio Jose Sanchez/AP)

Across the country, an estimated 90 percent of those in county jails don’t have health insurance. About the same number would qualify for subsidized health-care coverage under the Affordable Care Act. And those prisoners are more susceptible to chronic illnesses that, without treatment once they are freed, cost millions in emergency room visits.

Now, the San Francisco Sheriff’s Department thinks it can help cut costs — and reduce recidivism rates — by signing up many of the 31,000 people it books in jail every year for coverage under Obamacare.

On Tuesday, Sheriff Ross Mirkarimi introduced a bill before the city’s Board of Supervisors that would make his office responsible for helping inmates sign up for the Affordable Care Act. Mirkarimi’s office would need the bill to pass before it begins helping inmates with their applications.

Inmates in county jails already receive health care and substance abuse treatment. But that treatment ends the moment they leave prison. Signing inmates up for the Affordable Care Act or Medi-Cal, California’s version of Medicare, would provide that treatment after they leave prison.

Doing so could save the city big bucks. Mirkarimi estimated that San Francisco taxpayers could save about $2,500 per year for each inmate his office enrolls in insurance programs, whether through the state exchange or through Medi-Cal, which was expanded under the Affordable Care Act to cover individuals who make up to 138 percent of the federal poverty limit.

Many inmates could qualify for Medi-Cal, which covers anyone making less than $15,857 a year. Medi-Cal also covers mental health care and drug treatment, both of which could contribute to a drop in recidivism rates, Mirkarimi said. Those treatment programs alone could cut future repeat arrests by up to 20 percent.

“Enhancing access to integrated health care for the uninsured is not only a wise public health move, but it’s also wise public safety strategy — there is nexus between repeat incarceration and poor chronic health, especially people suffering with mental illness or substance addiction,” Mirkarimi told the board, according to the San Francisco Chronicle.