No, you won't need to purchase the state return again.
If you're using TurboTax Desktop and you delete your state return as suggested in the TurboTax Help article How do I clear my state return in the TurboTax for Windows software?, your state return will be deleted, but the state program that you purchased won't be.
If you're using TurboTax Online and you’ve already paid your state fees, you won't be able to delete your return, but you can start over by selecting Start Over next to your state return on the Status of your state returns screen. See the TurboTax Help article How do I delete my state return in TurboTax Online? for more information.
