If you live in California and work remotely for a company in Minnesota, all your income is taxed by your Resident State. If you paid tax to another state, CA will give you credit, so you don't get taxed twice on the same income.
You would not need to file a MN return, unless MN tax was withheld from your pay. If so, you can file a Non-Resident State Return to MN. Prepare your non-resident return first.
Here's How to File a Non-Resident State Return.
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