I live in California, I know in the county I live in if you go on welfare and the father of the child does not live in the same household as you and you need to apply for cash assistance they will automatically try to locate your bd and get him for Child support, food stamps however does not do that, nor does wic ... ( That's what happened to a friend of mine )
For wic it doesn't matter. I'm not sure what dcf is, but here in Alaska if you aren't living together the other parent has to pay child support.
If you don't want child support from him they won't make him... atleast not here in kentucky. They only make them pay child support here if you take them to court. He can still be on the birth certificate and everything. You need to go to your clinic and ask about applying for wic and everything. My friend is approved and her and her fiance plan on getting married. They just don't have good jobs atm and a very small place. Certain situations get first priority in the system but if you make an apointment they can help you out with all the paperwork right there.