You are a Michigan resident if Michigan is your permanent home. Your permanent home is the place you intend to return to whenever you go away. A temporary absence from Michigan, such as spending the winter in a southern state, does not make you a part-year resident. Income earned by a Michigan resident in a nonreciprocal state or Canadian province is taxed by Michigan, and may also be taxed by the other jurisdiction. If you pay tax to both, you can claim a credit on your Michigan Return.
You are a part-year resident if, during the year, you move your permanent home into or out of Michigan. You must pay Michigan income tax on income you earned, received or accrued while living in Michigan.
If you can't be considered as a resident or a nonresident, then your status for Michigan tax purpose is Nonresident. If you had income from Michigan sources but did not maintain a permanent home in Michigan, then you may fall under this category.