Yes, you will need to file both states if you won in Indiana and live in Michigan. You should file Indiana first as you may be able to get a small credit for taxes paid to other states on your Michigan return. But, you will be taxed by both states.
"If you were a full-year nonresident of Indiana, but received any income from Indiana sources, you must file your Indiana income taxes."https://www.in.gov/dor/4731.htm
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