Like sallye said.
From Michigan.gov:
Nursing Home, Home for the Aged and Adult Foster Care - If the facility pays local property taxes, you may claim your portion of those taxes for credit. You may not claim rent or monthly fees for the property tax credit amount. If both you and your spouse live in the facility, add your shares together.
If one spouse lives in a nursing home or foster care home and the other spouse maintains a home, you may file a joint credit claim. Combine the tax for the homestead and the share of the facility's property tax to compute your claim.
If you are single and maintain a homestead (that is not rented to someone else) while living in a nursing home or adult care facility, you may claim either your homestead or your share of the facility's property tax, but not both. Use the one that gives you the larger credit.