Does anyone know what the form needed to file with Missouri that is to be sent to the Division of Family Services with the Missouri return?

You may be referring to a checkbox at the top of many Missouri individual income tax forms.  You check this box to indicate you're attaching one or more Department of Social Services Eligibility forms.  See Form MO-1040A as an example.

According to Department of Social Services Form(s) in the Form MO-1040A Instructions:

Select the box at the top of the form indicating you have attached a Department of Social Services eligibility review form(s) (Temporary Assistance -TANF, Supplemental Nutrition Assistance Program - SNAP, MoHealth Benefits, and/or Childcare Subsidy Program) to your Missouri return. Failure to check this box may result in processing delays of benefit eligibility. For access to the Department of Social Service’s eligibility review form(s) visit: dor.mo.gov/taxation/individual/dss-forms.html. 

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