Hi Im in the military and was stationed in Michigan. I was wondering if my wife or I qualified for the homestead act since we rented a home in MI.

It depends, but you probably don't need to.  If your state of record is not Michigan, you will not need to file a Michigan tax return.  And your wife would only need to file a Michigan return if she never established residency in your state of record and worked in Michigan.  Please see this FAQ with more information (especially Joe and Mary example):  https://ttlc.intuit.com/replies/3302300.  

In addition, if your state of record is Michigan and your only income is military, Michigan does not tax active-duty income.  So really the only circumstance in which you will need the credit is if your wife is a Michigan resident because you are or she never established residency in your state of record and must file a Michigan resident return because of the presence test.