I have a particular state that I lived in asking for me to file with them. I'm in the military and my home of record is in a separate state. What to do?

Unfortunately, occasionally that happens, and you just have to provide them with the information they need indicating your HOR is some other state, and you had no MO-sourced income.

Some other states (CA in particular) have also been annoying out-of-state military personnel since they are all desperate for tax funds to keep them going.  I have a family member who was stationed in CA, and has since PCS'd out, but still gets occasional CA tax "requests"....but only because they bought a car while stationed in CA and it's titled/licensed there.

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MO does have an online non-filing form for non-MO military people, who are currently posted to MO, that supposedly prevents a future inquiry...BUT...it is not to be used if you already have a MO tax inquiry.  A current MO inquiry has to be handled separately.

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MO Military PERSONNEL tax brochure:

5735 - Tax Military Brochure (adobeconnect.com)

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MO non-resident Military "Online" No Return Required form.  (I have no idea if it is needed during every tax filing season, while stationed in MO, or not):

Missouri Department of Revenue | Military No Return Required (mo.gov)