It depends. TurboTax charges for the program at the point of e-filing, which is separate from any tax balance due that the state charges. If direct withdrawal was not authorized, then yes, you would need to mail a check in to your state.
Click the link for more details on getting back to your input to confirm what was set when you e-filed: How do I change my transferred direct deposit information?
To contact your state, follow this link: How do I contact my state Department of Revenue?
I also recommend looking to see if bank account information is included near the Tax Balance Due on your state return. If this information is not written on the return, then I suspect these details were set only for the Federal return, but I cannot see your return in this forum to confirm.
@colwas2002