Since you are residents of WI, all your income is taxable by WI, including your earnings from MN.
MN can tax the portion of your income earned from work physically performed from a location in MN. (e.g., if 60% of your income derives from work carried out within MN, then 60% of your work income will be taxable by MN).
WI will give you an "other state credit" for the taxes you pay to MN on the income taxed by both states.
Thus you should definitely request withholding for MN. Since the "other state credit" will reduce your WI tax bill significantly, whether or not you should also withhold for WI will depend on the actual numbers.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
