Yes, unfortunately, Michigan requires you to file as a nonresident and pay state income tax for the work you performed in the state, so you do have to file. You will be able to get the credit for tax paid to another state on your resident New York tax return. The credit applies because you are a NY resident who pays nonresident tax to Michigan. The convenience of the employer rule works to tax nonresident of New York whose employer is based in New York.
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