TurboTax does not receive any kind of tax refund, federal or state.
If you requested to have the TurboTax account fees deducted from your federal tax refund, the IRS will send the refund to a third party processor to have the fees and the service charge deducted. The third party processor will deduct the TurboTax fees plus the service charge and then attempt to direct deposit the remaining refund balance into the account that you entered on your tax return.
For the status of your tax refund you will need to contact the third party processor, Santa Barbara Tax Product Group, using their website - https://www.sbtpg.com/
Tax Products Group Contact Information - https://help.sbtpg.com/hc/en-us/articles/230084587-Contact-Information
If you weren't having any fees deducted from it then give it a few days to post. If your bank account number was wrong and the bank rejects the deposit the IRS will mail a check to the address on your return. That will take a couple weeks.