The issue is why you are living in Michigan while working for a New York company.
If you are in Michigan "for the convenience of the employer" - that is, because your employer wanted you there rather than in New York - then your wages would be taxable in Michigan.
However, for most employees in your situation who are living in another state for their own convenience and not at the employer's requirement, then you are required to report your wages as New York source income, taxable in New York on your NY nonresident return.
Do your NY return first, then do your Michigan resident return. In this way, your NY tax will find its way to line 18 on your Michigan MI-1040, to reduce your Michigan tax owed.
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