Mich. Comp. Laws § 780.171: Nullification of support orders; crediting amounts paid.

Sec. 21.

A support order made by a court of this state pursuant to this act does not nullify and is not nullified by a support order made by a court of this state pursuant to any other law or by a support order made by a court of any other state pursuant to a substantially similar act or any other law, regardless of priority of issuance, unless otherwise specifically provided by the court. Amounts paid for a particular period pursuant to any support order made by the court of another state shall be credited against the amounts accruing or accrued for the same period under any support order made by the court of this state.