What I assume that happened is that your employer withheld money and sent it to Michigan instead of another state. If so, that wasn't Michigan taxing you but your employer sending your money to the wrong state.
Did you work in Michigan? If so, then Michigan has the right to tax you for work done there.
Unfortunately, if the employer made a mistake, they can't get your money back. You will have to file a Michigan non-resident return to recover your errant withholding.
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