If your spouse earned income from Minnesota while living there, she would file a Part Year Resident MN return and report all the MN income. She will be able to indicate how much of that income was earned while living in another state (Wisconsin). She would also file a Part-Year Wisconsin Resident return, and report the income earned from MN while living there. WI will give credit for tax paid on that income to MN, so she is not double-taxed on that portion of her income.
Pay close attention when preparing your state returns to the dates moved in/out of each state for your spouse, especially if you're filing a joint return.
Here's details about Allocating Income for a Part-Year Resident and also on How to File a Part-Year Resident Return.
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