Mich. Comp. Laws § 450.4208

Sec. 208. (1) A resident agent of a limited liability company may resign as agent upon filing a written notice of resignation with the administrator and with a member or manager of the limited liability company. (2) The company shall promptly appoint a successor resident agent. (3) The appointment of the resigning agent terminates 30 days after the date the notice is filed with the administrator or upon the appointment of a successor, whichever occurs first.