If I decide to file Federal, then later State tax with TurboTax, does it cost extra to use TurboTax instead of filing both Federal and State at the same time?

[DoninGA]

No, there is no additional fee to e-file the state tax return after the federal tax return.  Using the TurboTax online editions there are no e-file fees, federal or state.  You only pay for the usage of the federal and state software if not using the Free online edition.