If you choose to e-file your federal first, you'll have to wait until that return has been accepted before you can e-file your state.
If your federal hasn't been accepted, or you printed and mailed it, you won't be able to e-file your state but you can print and mail a paper return.
Married filers: If you e-filed your federal using the joint married status, but you want to e-file your state returns separately, only one of you will be able to e-file. The other must paper-file their state return.