Mich. Comp. Laws § 400.66b
The county social welfare board shall require the county department to act promptly on all applications for hospitalization and shall provide for retroactive authorizations for emergency care in accordance with rules which the board shall establish including one defining "emergency". When the person hospitalized in an emergency is found to be eligible for hospitalization at public expense under section 66a of this act and is found to be a transient in the county with a domicile elsewhere in the state, the county in which his domicile is located shall be responsible for the cost of hospitalization to the county department which has authorized the care. When a patient is taken without authorization in an emergency across a county line to a hospital in a county other than the county of domicile of the patient, the county department in which the emergency occurred shall be responsible, in accordance with its own rules governing emergency care, to the hospital for the expense of the emergency care subject to reimbursement by the county of domicile as provided by this section. The state department shall provide rules governing intercounty payments and shall arbitrate and decide disputes arising thereunder.
MCL 400.66b