Your state return will not be e-filed until your Federal return is accepted (not just transmitted) by the IRS. Essentially, you e-file both returns to the IRS when you transmit through TurboTax, and the IRS electronically forwards your state return to the tax authority in your state.
Please see this link to make sure your state is one that can be e-filed, scroll down about halfway:
https://turbotax.intuit.com/tax-tips/e-file/e-file-income-tax-return-electronic-filing/L9DnoQ39y
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