Yes, your federal and state returns are separate returns sent to different agencies. It's possible for your federal to be accepted and your state to be pending, or rejected.
Sign in to your TurboTax account and check to see the status of your state return. If it says Ready to mail, you finished your state return, but didn't e-file it. In that case, you need to select Add State, then Review your return, and go through the File section again to finish filing.
If it says Rejected, you need to select Fix my return and make whatever correction it says.
If it says Accepted, make sure you have the correct amount for your refund. If you ask for your refund status, but don't have the right refund amount, the state will say that they don't have it.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"