Ohio taxes all income as a resident. Some states require a return if the income is sourced from that state, like stock from a former employer. MI taxes MI sourced income so you may need to file a tax return. If it is generic investments from anywhere, MI does not have a claim to tax the income.
MI may ask questions depending on the amount even if you don't have to file.
See the bottom right of page 3 for filing requirements for MI at MI-1040 Book with forms with reference to pages 48 and 59 for MI sourced income.
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