Can I file my state return separate from my federal?

Yes. You can file them separately. Although state returns can be e-filed with your federal return (or after your federal return has already been accepted), it's no longer possible to e-file state returns before the federal.

They are taking this measure to add an extra layer of security to all e-filed state returns.

This new requirement also means you won't be able to e-file your state if your federal return was, or will be, paper-filed.

You can file federal now and skip state filing, but your e-filed federal return will need to be accepted before you can e-file your state (or, you can just paper-file your state return later. More info)

Here are two ways to skip your state in TurboTax Online:

1. Delete your state return, file your federal return now, and then come back later re-do your state return; or
2. Pay for both your federal and state returns now, and when you get to the Let's get ready to e-file screen, select the File by mail button and click the I'm not ready to file radio button below your state and click save.

Method 1 doesn't require up-front payment for your state, but you'll have to re-enter your state information. Method 2 saves the work you did on your state return but requires up-front payment.