The change is part of legislation passed this year as a way to cut costs at the state Department of Corrections.
More than 100 corrections officers were laid off last week as a way to save more than $3 million.
The change also means counties will be picking up more of the costs of medical care for state inmates.
However, some sheriffs have said they are having problems finding doctors willing to treat inmates at the Medicaid reimbursement rate. That means the county may have to pick up the remaining tab of whatever the state won't pay.
By law, the county and the state are required to provide medical care for inmates. Many counties and the state have turned to managed care companies to help keep costs down.