Mich. Comp. Laws § 331.207
Any person afflicted with a contagious or infectious disease, for whose treatment and care the county maintaining such hospital or institution is responsible, shall be admitted to such hospital or institution upon the certificate of the health officer of such county.
Any indigent person suffering from any physical ailment or impairment for whose treatment and care the county maintaining such hospital or institution, or any township or city therein, is responsible, shall be admitted to such hospital or institution upon the order of the social welfare board of said county.
If the facilities of the hospital or institution will permit, the board of trustees, in its discretion, may accept other persons afflicted with contagious or infectious diseases and other indigent persons suffering from any physical ailment or impairment, and for temporary detention of mentally ill patients, both non-indigent and indigent, and upon such terms and conditions as may be fixed by the board of supervisors of the county.
The board of trustees may make regulations governing the conduct of patients and may exclude any person or persons wilfully violating such regulations.
MCL 331.207