You would have to complete the federal return and mark it to be mailed, then not mail the federal and just mail the state. You could not efile just the state.
To efile the state thru the TT system you had to already successfully efiled the federal return thru the TT system.
You say you already filed a federal return but do not tell us if you used TurboTax for the federal return. When you use TurboTax the information flows from the federal return to the state return. You cannot use this software to prepare only a "stand alone" state return. If you used some other software for your state then you should go back to that same program for your state return, or perhaps use the state's own site to prepare the return.
If you used TurboTax for your federal return then go back to your account, and click on Add a State to prepare a state return. A state return can only be e-filed if you successfully e-filed a federal return that was accepted. Otherwise you will have to mail your state return.