Mi has a reciprocal agreement, on wages, with IN. No MI state taxes are withheld or due and you do not normally need to file a MI return. But IN will tax you on your other state income.
If MI taxes are mistakenly withheld, you then have to file a MI return to get a full refund*. IN will not give you a credit.
Michigan is particularly messy to get a refund from. For details, see:
https://ttlc.intuit.com/community/state-taxes/discussion/re-state-tax/01/1501675#M67119
*However the reciprocity agreement does not apply to local city taxes. You are not required to file a MI city return, but you are also not entitled to a refund of the city withholding (box19 on your W-2), unless there was an error in the amount. Some (but not all) IN counties (but not the state) allow a credit, or partial credit for tax paid to a MI city. If yours is one, that will come up in the IN state interview.
