I am using turbotax self-employed version, how can I e-file my state return since I did not see any words mentioning the state is e-file

[Kat]

Most users e-file both federal and state returns at the same time.  However, if you somehow failed to e-file your state return, you can still do that.  You'll just have to wait until the federal return has been "Accepted" by the IRS.  For instructions on how to e-file your state return after your federal has been accepted, see the info linked below.

How do I e-file my state after I already filed my federal? 

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