This is how Missouri calculates nonresident tax. Missouri will pretend that all of your income is taxable in Missouri, and calculate what your tax would be. Then Missouri prorates the amount of tax liability to the percentage of income actually earned in Missouri. This is why you see the percentages you mention. Since your husband did not work in Missouri, he has a 0% income percentage, because none of his income is earned in Missouri. The 44% represents the percentage of the total income earned in Missouri.
For an explanation of this, please click on this link: Filing Form MO-CR or Form MO-NRI. You will notice this excerpt:
Regardless of where your income was earned or if you are using Form MO-CR or Form MO-NRI, you must begin the Missouri return with your federal adjusted gross income, as reported on your federal return. Next, apply all allowable deductions and compute the tax on all of your income. The tax is then reduced by either the Missouri resident credit (Form MO-CR) or the Missouri income percentage (Form MO-NRI). The result for nonresidents is a prorated Missouri income tax based only on the income earned in Missouri. The result for part-year residents is a prorated income tax based only on the income earned while a Missouri resident. (All Italics added).
Yes, this can increase your tax by putting you in higher tax brackets on income not earned in Missouri. But that is how Missouri (and a number of states) tax nonresidents (and part-year residents).
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