If you chose to e-file your federal return on the File section then yes your federal is e-file even if you mail the state tax return.
When you sign in again to TurboTax the screen you get when you have e-file is the Federal return status.
If you e-filed your tax return you can check the e-file status with this link: https://turbotax.intuit.com/tax-tools/efile-status-lookup/
What does the status show under your Federal return when you log in? You have to manually click Transmit Returns to e-file your return.
Under the page titled"Here Are Your Filing Choices" it says 2016 Federal Tax Return: E-File...and....2016 State Tax Return: File By Mail. I cannot get to a page that says Transmit Returns. Do I need to log out and log back in?
Okay, that means your federal is going to be e-filed and you chose to print and mail your state return. If you want to change the state to e-file, just click "I'd like to change filing methods" on that page. Then change your filing method to "E-file" for the state return and click Save. Then continue through to e-file it and you should see Transmit returns button then.
If you chose to e-file your federal return on the File section then yes your federal is e-file even if you mail the state tax return.
When you sign in again to TurboTax the screen you get when you have e-file is the Federal return status.
If you e-filed your tax return you can check the e-file status with this link: https://turbotax.intuit.com/tax-tools/efile-status-lookup/