I live in Ohio on the Michigan border. I want to start a business in Michigan but must be a Michigan resident to do so. I do not intend to move to Michigan. How can I do this if I can be a resident of only one state?

You would have to move to Michigan if you are REQUIRED to be a Michigan resident. I see no way around that. You could have two addresses in two different States, of course, but that would not change your residency.

You would need to establish a residence in Michigan and make it your primary. However, from what little we know it sounds like you for not really plan to be a resident, right?