You cannot file just your state taxes with TurboTax.
"The TurboTax state program is designed to transfer information from your federal return. For this reason, TurboTax state isn't sold as a standalone tax-preparation product. You can use TurboTax to prepare and file your federal return without your state—but not the other way around."
Reference: Can I prepare and file just my state return using TurboTax?