You do not have to file a Missouri return if you are not required to file a federal return.
If you are required to file a federal return, you may not have to file a Missouri return if:
Note: If you are not required to file a Missouri return, but you received a W-2 form stating you had Missouri tax withheld, you must file a Missouri return to get a refund of your Missouri withholding. If you are not required to file a Missouri return and you do not anticipate an increase in income, you may change your W-4 form to "exempt" so your employer will not withhold Missouri tax.
This information can also be found on the Missouri Form 1040 Instructions available on the Missouri Department of Revenue website.