Moving out of Michigan is easy. Stopping Michigan taxes is a different act, and it happens on paper: Michigan keeps treating you as a resident until the record shows otherwise.
On the burden of showing otherwise: By statute, domicile continues until another permanent establishment is established — the facts creating the new home decide the change, and the party asserting it supplies them.
Two tests decide it. Cross 183 days with a Michigan abode still available and you are taxed as a resident regardless of where you claim to live — and see day-counting rules. Or keep the day count clean but leave the life-pattern evidence pointing at Michigan, and domicile does the same work. Everything on this page exists to answer one question: if Treasury asks, does your record hold?