Can you clarify the situation a little bit? Did you keep the same job after you moved? What state did you move to? Were you still physically working in Michigan or telecommuting?
Generally Michigan will not tax your income after you move unless you are still working within their borders. Even then, you should not be taxed by Michigan if you moved to a neighboring state with a reciprocal agreement.
This can be fixed in your part-year tax return for Michigan by only allocating the wages that were earned while you were a Michigan resident. The remainder of the wages should be allocated to your new state and you will have to pay taxes to the new state for the wages earned during that period. If your employer withheld Michigan taxes the entire year and you only had to pay for them for the time you were a Michigan resident, then you will probably get a refund from Michigan. You will also want to let your employer know that you moved so they start withholding taxes from the correct state.
