If you are being married in the State of Michigan, you will obtain your marraige license in accordance with your legal residence.
If BOTH the bride and groom legally reside outside of the State of Michigan, you will apply for the Marriage License in the County in which the marriage is taking place.
If EITHER the bride or groom legally redside in the State of Michigan, you will apply for the Marriage License in the County of that legal residence. The marriage can be performed anywhere in the State.
If BOTH the bride and groom reside in the State of Michigan, you may apply for your Marriage License in EITHER County in which the bride or groom legally reside. The marriage can be performed anywhere in the State.
Note that it does not matter where you actually live. You must go by your legal address.
Note too that if you are wishing to be married by a Person of the Courts, the County in which you apply for your Marriage License will tell you WHICH court you must go to for your marraige to take place. This too depends on your legal residence.
Please click on the following link for specific information regarding how to apply for your Marriage License.
Michigan Marriage Laws