The easiest way is to look at your w-2 to see how much income was reported to MN. This is the income reported to the other state. Then, the tax would be the difference of the amount of MN tax withheld and the amount of refund you receive from MN. So if you paid 900 in MN tax, and got a refund of 200, your MN tax on MN income is 700. However, if you had 100 additional to pay, then your MN tax is 1000 (900 withheld plus the 100 due). However, if you are getting back all of your taxes from MN, then you will not get any credit for taxes paid to MN because you would have zero tax liability with MN.
If you have not done so, it is recommended to prepare the MN nonresident return first to make sure that these credits are correctly calculated.
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