No. You do not need to file a MN return if your MN gross income calculated according to this link (extracted below) is below $13,825. Yes, you are correct to allocate to IA only the income that belongs to IA. As long as you have documentation showing the move to MN and your calculations for the allocation you are good to go.
"Step 1:
Calculate your total income received while you were a Minnesota resident. Use your income from all sources, including income received outside of Minnesota.
Step 2:
Calculate your total Minnesota income received while you were a nonresident. This includes:
- Wages, salaries, fees, commissions, tips, and bonuses for work done in Minnesota.
- Gross rents and royalties from Minnesota property.
- Gains from the sale of land or other tangible property in Minnesota.
- Gross winnings from gambling in Minnesota.
- Gains from the sale of a partnership interest that had property or sales in Minnesota.
- Gains on the sale of goodwill or income from a “non-compete” agreement connected with a business operating in Minnesota.
- Minnesota gross income from a business or profession conducted partly or entirely in Minnesota.
Step 3:
Combine the totals from steps 1 and 2."
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