Yes, you can file your state return after your federal return has been accepted. Here is a link with instructions (extracted below).
I did that but it bring me through all of the audit stuff, then dumps me to 'let's get ready to file your taxes'. When I hit continue to brings me to e-file my federal return.
Try closing TurboTax, clear your Cache and Cookies if you are using TurboTax Online, and reopen TurboTax. You can also try a different browser.
Also, make sure you have ran all updates.
If using TurboTax Online: Clear your cache and cookies. See this FAQ, for your particular browser.
If using TurboTax Desktop: Please see this FAQ.