Part-year residents and nonresidents of Minnesota calculate their tax on taxable income from all sources, just like full-year residents do.
However, Minnesota tax is then prorated. The proration is based on the ratio of your modified Minnesota adjusted gross income (AGI) to your modified AGI from all sources. So, your Minnesota tax will be based on your Minnesota AGI, not from your total AGI.
This proration is calculated on Minnesota Schedule M1NR, Nonresidents/Part-Year Residents, and the prorated tax amount is carried from line 32 of that form to line 13 of Form M1, Individual Income Tax.