It depends. Based on the information you provide in your question, it sounds like you should be filing part-year resident returns for both Michigan and Vermont.
Vermont, and a number of other states, have a similar criteria for determining a statutory resident. A statutory resident is someone who maintains a domicile in the state (even though it is not the main place in which they live), and is physically present in the state, typically for 183 days. However, when someone moves into the state to become a "domiciliary resident" (where your main home is located), they file as a part-year resident even though the period of residency in the state is more than 183 days.
Your question seems to indicate that this is the case with you. If you did move into Vermont (and did not previously have a domicile there prior to your move), you file part-year resident returns for each state, and Michigan will tax the Michigan income while Vermont will tax the Vermont income.
However, if you were a full-year Vermont resident, you would need to file a Michigan nonresident return and a Vermont resident return. In this circumstance your income is not excluded from Vermont. However, Vermont would provide you with a credit for the tax you pay to Michigan for the income you earn there. You would want to prepare the Michigan return first so that the credit for the taxes paid can be transferred over to your Vermont return.
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