Does your state return shows as "Pending?" If so, some of the states don't start processing returns at the same as the IRS, they start later. It's not uncommon for your state return to show pending for days after your federal return has been accepted by the IRS. You generally see this a lot when you e-file when e-filing first opens in January or early February. Just keep an eye on it, it will move along if still shows pending. See here for how to track it How do I track my state refund?

If your state return still shows as "Started," and federal return has already been accepted by the IRS (not accepted by TurboTax), you just need to go back in and re-submit that state return. This can happen if some of your state forms were not finalized when you tried to e-file your state at the same time as e-filing your Federal return. 

You can use the instructions below to help you re-submit the state return. 

TurboTax Online Detailed Instructions:

• Login to your TurboTax account.
• Select Show on your Tax Home screen, then Your tax returns and documents.
• Make sure the current tax year is highlighted, then select Add a state.
• Select the State Taxes tab.
• Select Continue to start or complete your state taxes.
• Select Done with State.
• Continue through the flow to review and file your state taxes.

TurboTax CD/Download Detailed Instructions:

• Open your return.
• Click on State Taxes tab.
• Follow on screen prompts and continue through the flow to review and file your state taxes.