It depends -
If you are still considered an MI resident, then you would need to file an MI resident state income tax return even if all your income was earned outside the country. However, you would only need to include any foreign earned income that is not excluded under the Foreign
Earned Income Exclusion
This is from the MI Department of Revenue -
Is my foreign income subject to Michigan tax?
Yes. Any portion of the foreign income included in adjusted gross income is subject to Michigan tax.
Note: You must include all foreign income in your total household resources
If you left MI, do not have any ties to MI and do not intend to return to MI, then no MI state return is required.