It depends, but you may not be able to claim the credit in either state. You are a Minnesota Resident, so, to claim the credit in Minnesota, your residence also must be in Minnesota, according to this MN website: http://www.revenue.state.mn.us/individuals/prop_tax_refund/Pages/Eligibility_Requirements_for_the_Pr.... However, if you do have a residence you are maintaining in Minnesota, then you may claim the credit.
You are a Wisconsin nonresident, because your presence in Wisconsin is a temporary absence while you are in school. To receive the homestead credit in Wisconsin, you are required to be a full-year resident of Wisconsin. This WI website has more information: https://www.revenue.wi.gov/Pages/FAQS/ise-home.aspx
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