If you did not file a federal return with TurboTax, you are not able to e-file just the state in TurboTax since it pulls information from the federal return. You can recreate your federal in TurboTax to generate the state but you'd have to print and mail the state return.
The other option you have would be to go to your state's website and file through their filing service. Or you can print the tax forms from their sites and complete them by hand to mail to them. See below for further details on this.
Can I prepare and file just my state return using TurboTax?