The short answer is Yes. For 2016 you are a part-year resident of Michigan and so must file a Michigan return.
- Determine the last day of your Michigan residency - usually this is the day before the day you moved into your Washington home for good - it depends on the exact facts
- Your Michigan return will include income received in 2016 through your last day of residency in Michigabn, including pension income, bank interest, dividends, etc.
- Income payments received after your first day of residence in Washington are not taxable by Michigan, even if they are from Michigan firms or the Michigan government.
- You report the allocation of income between Washington and Michigan on Michigan Schedule NR
Reference: instructions for Michigan Schedule NR
Part-year returns can be tricky, and you may want to have yours done by a professional preparer, just for this year.