It depends.
If you received any unemployment income in 2020 from Minnesota, then yes, you potentially will need to pay taxes on the unemployment income as Minnesota does tax unemployment income.
Assuming you received unemployment from Minnesota in 2020 while you were a nonresident of the state, you would only need to file a tax return if your gross income was at least $12,400.
Please see the following link for more information to help you determine if you would have been considered a resident or nonresident of Minnesota.
MN Nonresident filing requirement
You will be able to claim a credit on your Iowa tax return for any taxes paid in MN on the unemployment income. Just be sure to complete your nonresident state tax return (MN) first and then proceed with your resident (IA) state tax return to ensure all of the credits are calculated correctly.
If you are asking about your 2019 income tax return, it sounds like you lived and worked in Minnesota for the entire year. If this is the case, you would still need to file your MN income tax return and report any unemployment income earned in 2019 in MN. You would not have any filing requirements in Iowa if you did not reside there during 2019.
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