No - You do not have to file a MO return at all. According to the MO Department of Revenue website, Remote Work Resources:
My residency is outside of Missouri. I am performing "remote work" for my Missouri-based employer. Am I obligated to withhold Missouri tax from my wages?
No. If a non-resident employee performs all of his or her services outside of Missouri, the wages paid to that employee are not subject to Missouri taxes.
For additional information, refer to the withholding tax frequently asked questions web page.
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