Not really.  If you didn't use Turbo Tax to do your federal return, you would first have to fill out a federal return (don't file it) to match the real return you did file and you would have to pay for federal for it to flow into the state return.  Then you would have to mail the state.
https://ttlc.intuit.com/questions/2580110-can-i-prepare-and-file-just-my-state-return-using-turbotax