Mich. Comp. Laws § 720.204

Sec. 4. Whenever the state public administrator shall file with the probate court of any county a copy, certified by said state public administrator, of the appointment of a county public administrator to act in the county in which the certificate is so filed, then letters of administration may, instead of being issued and granted to the state public administrator, be granted and issued to such county public administrator, and he shall be entitled to receive the same at any time that his appointment as such remains in full force and effect.