You should file as a MN resident and report the WI income on a WI Non-resident return.
MN will tax you on all of your income, but give you a tax credit for the taxes paid to WI.
Be sure you do your WI first so the credit will flow properly to your MN return.
Most states follow the same rules for residency. Where are you registered to vote, where is your driver's license issued, car insurance, etc.
It's easy to get crossed up and wind up paying penalties when you consider yourself a resident of one state and the facts and circumstances prove something else.