Each state has different procedures on how they process a state tax return.
Did you e-file your tax return and was it accepted?
You complete your tax return by finishing all 3 Steps in the File section. In Step 3, to e-file your tax return, you must click on the large Orange button labeled "Transmit my returns now".
After completing the File section and e-filing your tax return you will receive two emails from TurboTax. The first email when your tax return was transmitted and the second email when the tax return has either been accepted or rejected.
To check the status of an e-filed return, open up your desktop product or log into your TurboTax Online Account. You can find your status within the TurboTax product.
If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
See this TurboTax support FAQ for contacting a state department of revenue - https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/0...
Did you mail the state return to the correct state address? If you put the state tax return in the same envelope with your federal return--as we have seen some users do by mistake -- then the IRS would just toss out your state return. If you made that mistake you will need to print it again and mail it to the right address.
Are you sure it was the Federal refund you got and not the state? The IRS was not been processing mailed returns and is now working on the backlog that's been stacking up. They are opening the mail in order so if you mailed in July it should take a long time for Federal. See this IRS page for the latest information
Almost Everyone who mailed has been getting their state refund first.