Mich. Comp. Laws § 772.15

Sec. 15. A surety in a recognizance to keep the peace has the same authority and right to take and surrender the principal as in other criminal cases. Upon the surrender the surety shall be discharged and exempt from all liability for an act of the principal subsequent to the surrender that would be a breach of the condition of the recognizance. The surety is not discharged or exempt from liability for costs on an appeal taken by the principal in the recognizance. The person surrendered by a surety may recognize anew, with sufficient sureties, before a judge of the same court for the remainder of the term, and, upon doing so, shall be discharged from custody.