Probably. Illinois and Michigan are both flat tax states with similar tax rates (4.95% for IL and 4.25% for MI). Since the IL rate is higher, your IL refund will probably cover the tax due to MI. Some deductions and credits are different, but it should balance out.
IL and MI are reciprocal states so you should have MI tax withheld from your pay. That way you’ll only have to file one tax return (assuming your job is your only IL income).
You can file a IL-5-NR with your employer.
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