No, you do not have to file as married filing jointly to claim the Michigan homestead property tax credit. According to the Michigan Department of Revenue, spouses who file separate Michigan income tax returns but shared a homestead for the entire year are entitled to one property tax credit. The credit claim must be based on the total household resources of both spouses during the time the homestead was shared.
Please view page 4 in the Michigan link below for more information about this rule.
https://www.michigan.gov/documents/taxes/MI-1040CR_Instructions_477247_7.pdf