Mich. Comp. Laws § 38.24

Sec. 24. (1) Except as may otherwise be provided in sections 33 and 34, a member who becomes totally incapacitated for duty because of a personal injury or disease that is not the natural and proximate result of the member's performance of duty may be retired if all of the following apply: (a) The member, the member's personal representative or guardian, the member's department head, or the state personnel director files an application on behalf of the member with the retirement board no later than 1 year after termination of the member's state employment. (b) A medical advisor conducts a medical examination of the member and certifies in writing that the member is mentally or physically totally incapacitated for further performance of duty, that the incapacitation is likely to be permanent, and that the member should be retired. (c) The member has been a state employee for at least 10 years. (2) Upon appeal to the retirement board, the retirement board, for good cause, may accept an application for a disability retirement allowance not later than 2 years after termination of the member's state employment.