You will file as part-year residents of each state. In the state section, you will need to adjust the income to be taxed to MN so it only includes the amount you earned while either living there and/or working in that state. Prepare the MN return first as you may be able to get a credit for taxes paid to both states.
To avoid future underpayment penalties, you can make estimated tax payments to WI. The following link has some FAQs about how to pay those https://www.revenue.wi.gov/pages/faqs/pcs-estpay.aspx
Also, see if you can change your W-4 with your MN employer to be "exempt" or to have the least amount of taxes withheld as possible so you are paying out double during the entire year. This should be done unless you actually work in MN. In that case, the employer should be withholding MN taxes.
How do I file if I moved to a different
state last year?
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