Mich. Comp. Laws § 773.11

Sec. 11. The expenses and fees of the inquest shall be paid from the general fund of the county in which the inquisition was taken. When an inquest is held for a person who died in a prison or public reformatory of this state, the expense of the inquest shall be audited and paid by the institution, in the same manner as other charges against the institution are audited and paid.