First, if you haven't already done so, submit Michigan Form MI-W4 to your employer so that they can cease withholding Michigan taxes. Here's a link to that form: https://www.michigan.gov/documents/mw4f_76761_7.pdf
Second, in order to receive a refund of the incorrectly withheld Michigan taxes, you must submit a Michigan Non-resident tax return, showing zero Michigan income. This TurboTax FAQ explains how to do that: https://ttlc.intuit.com/questions/1901271-how-do-i-file-a-nonresident-state-return
Finally, if your employer is unable to withhold MA taxes, you should consider making estimated tax payments to MA as long as you are in this situation.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
