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.
This adds an extra layer of security to all e-filed state returns. This also means you won't be able to e-file your state if your federal return was, or will be, paper-filed.
If you e-filed your federal return as Married Filing Jointly, but want to file your state returns as Married Filing Separately, only one state return can be e-filed. The other will have to be paper-filed.
Federal returns are not affected by this security measure and can be e-filed with or without a state.
If you mail your federal tax return, you will have to mail your state return as well.