Two things: Minnesota requires you to use the same filing status as your Federal return (as a Minnesota resident) and also taxes all of your income. Since you also must pay tax on the income you earned in New Mexico to New Mexico, Minnesota will give you a credit for the tax you pay to New Mexico on that income. But that credit is limited to the amount that Minnesota will tax the same income.
We don't have access to your return or account to know exactly what you are seeing, but hopefully this gives some context. You can certainly provide additional details with hypothetical numbers/information to provide you a more detailed response as well.
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