You should get screens in the Michigan interview that display 'Federal Amount' and either 'Non-Michigan Amount' or 'Michigan Amount' where you can enter a different number for income items, like Dividends.
The amount would be shown on the Federal 1099-DIV Worksheet, Box 1a, U.S. Government Interest. You may want to review your 1099-Div entry in your Federal return to make sure the amount is entered there.
Click this link for more info on Allocating Income as a Part-Year Resident.
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