The word "state" is not enough info. That can be interpreted a couple of different ways. Please explain more about what that means. And what are you referring to when you said "chose to pay it online"--did you have some product fees, or did you have state taxes due?
Did you use Free Edition? That's what is indicated under your question. Is that correct? If so, there shouldn't be any product fees in Free Edition. So are you asking about state taxes due? It's not possible to pay any state taxes due out of a Federal refund.
So until you explain more, we don't know for sure what you mean and are experiencing.
Or are you referring to a "net amount" displayed at the Tax Home--a figure that represents the total of the Federal refund minus the state taxes due? If so, that's just provided for your information to show you the net amount you are left with when all is said and done, taking both the Federal and state situations into consideration. That doesn't mean any state tax due is paid out of the Federal refund (which cannot be done.) You have to pay any state taxes due by using whatever method your state allows (can vary from state to state). TurboTax should have told you of the state tax payment options for your particular state.