Mich. Comp. Laws § 38.1383

Sec. 83. (1) Each retirement allowance shall date from the first of the month following the month in which the applicant satisfies the age and service requirements of this act and terminated reporting unit service, but not more than 12 months before the month in which the application was filed with the retirement system, if the applicant satisfies the legal requirements for the retirement allowance at the time the application is filed. (2) A full month's retirement allowance shall be payable for the month in which a retirant or retirement allowance beneficiary ceases to be eligible for continuation of benefits. If eligibility ceases because of death, the payment shall be made to the retirement allowance beneficiary, if any, or to the deceased recipient's estate or to the legal representative of the deceased recipient.