Yes, you need to file a Michigan Nonresident return. Here is what the Michigan Department of Revenue states:
Bonus pay, severance pay, deferred income, and any other amount accrued while a Michigan resident are subject to Michigan tax no matter where you lived when you received it.
Use Schedule NR to figure your Michigan taxable income. You must pay Michigan income tax on the following types of income:
Salary, wages, and other employee compensation for work performed in Michigan.
Income (including dividend and interest income) from an S corporation, partnership or an unincorporated business, or other business activity in Michigan.
Here is the link to the Michigan instructions:
https://www.michigan.gov/documents/taxes/MI-1040_Book_no_forms_642357_7.pdf
