Michigan DOES tax the earnings of a non-qualified distribution.
Michigan instructs you to ADD BACK TO INCOME the earnings portion of that non-qualified distribution if it is not included in your Federal AGI.
The non-qualified distribution (Form 1099-Q) WAS taxed and the earnings portion is included in your Federal AGI, so no additional add-back is needed for the earnings on that distribution, however, if you took a Michigan State tax break for making a contribution, an adjustment for a return of that contribution may be needed for your Michigan State return since the Federal return would not adjust for that.
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