TurboTax recommends filing both federal and state returns at the same time. But it's not a big deal. You'll just need to wait until your federal return has been accepted, then go back and e-file your state return. See instructions on how to proceed in the TurboTax FAQ below.
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*** I am NOT a tax expert. I am a seasoned TurboTax user, and volunteer to provide assistance to TT users. Nothing I post is to be considered TAX ADVICE; I bear no legal liability for responses.***