You're a citizen of the U.S. of A.
You may be a resident of one or more than one state.
If you want to keep your "residency" in Ohio, just keep getting formal mail there, i.e. insurance, college correspondence, etc.
For insurance reasons, that should be good enough. They won't know that you have a MI driver's license, should you decide to go that route.
Not to mention that if health care is your only reason for this question, you'll likely lose the health care through your parents because of age or loss of student status before you really have to decide between residency in one state over another (for the purpose of driver's license, CCW permit, etc.)