If you're just filing your state taxes by themselves (no federal) you won't be able to do this in TurboTax. For security reasons, the state must be e-filed concurrently with the federal, or after the federal has been accepted. You can try visiting your state's Department of Revenue website to see if they offer an online filing option (many states do).
Otherwise, if you are also filing your federal with TurboTax, you ought to be able to e-file your state UNLESS there's some state tax form that can only be paper-filed. We'll let you know.
