While the specifics can vary by state, generally, homestead exemptions are only available for an individual or family's primary residence. This means you cannot claim homestead exemptions in multiple states.
Homestead Exemption: Every person who has legal or equitable title to real property in the State of Florida and who resides thereon and in good faith makes it his or her permanent home is eligible to receive a homestead exemption of up to $50,000.
You can claim a property tax credit if all the following apply: Your homestead is in Michigan (whether you rent or own). You were a Michigan Resident for at least 6 months of the year you are filing in. You have Total Household Resources (THR) under a specified amount adjusted annually.
At any given time, you can only have one domicile. However, that doesn't mean that another state can't claim you as a resident for tax reasons.