Not allowed, unless licensed as an ORV and that particular State Park is ALSO open to ORVs (only a few are).
https://www.michigan.gov/documents/dnr/Chapter_IX_December_20_2017_609878_7.pdf
9.18 State parks and recreation areas, certain conduct prohibited.
Order 9.18 A person shall not do any of the following in any state park or recreation area:
(2) Operate an unlicensed, wheeled motorized device capable of transporting a person on a park road or parking
lot, unless otherwise permitted by posted notice. Use of such devices shall be permitted for individuals with mobility
impairments.