If it is determined I owe no taxes in non-resident state, do I need to file for that state?

Here are Minnesota's rules:

Nonresidents : If you were a resident of another state but lived in Minnesota, file a Minnesota income tax return as a Minnesota resident if both of these conditions applied to you:

• You were in Minnesota for 183 days or more during the tax year

• You or your spouse owned, rented, lived in, or leased an abode (house, townhouse, condominium, apartment, mobile home, or cabin, with cooking and bathing facilities in Minnesota, that could be lived in year-round)

If both conditions apply, you are considered a Minnesota resident for the length of time you maintained an abode in Minnesota. File a Minnesota income tax return if you meet the filing requirements in the next section. 

Filing Requirements for Part-Year Residents and Nonresidents

1.  Determine your total income from all sources (including sources not in Minnesota) while a Minnesota resident.

2.  Determine the total of the following types of income you received while a nonresident of Minnesota:

•  Wages, salaries, fees, commissions, tips or bonuses for work done in Minnesota

•  Gross rents and royalties received from property located in Minnesota

•  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, to the extent the partnership had property or sales in Minnesota

•  Gains on the sale of goodwill or income from an agreement not to compete connected with a business operating in Minnesota

•  Minnesota gross income from a business or profession conducted partly or entirely in Minnesota. This is the amount from line 7 of federal Schedule C, line 1 of Schedule C-EZ, or line 9 of Schedule F of Form 1040. Gross income from a partnership, S corporation, or Trust or Estate is the amount on line 19 of Schedule KPI, line 19 of Schedule KS, or line 25 of Schedule KF.

3.  Add step 1 and step 2. If the total is $10,350 or more, you must file a Minnesota income tax return and Schedule M1NR. If the result is less than $10,350 and you had amounts withheld or paid estimated tax, file a Minnesota income tax return and Schedule M1NR to receive a refund. Even if only one spouse has Minnesota income and you filed a joint federal return, you must file a joint Minnesota income tax return. Complete Schedule M1NR and include a copy of the schedule when you file your return.