You didn't mention the particular state, but here's some information about state refunds in general and how to check on yours.
First, you need to be sure your state return was successfully filed. If you efiled, be sure your efiled state return was accepted. If you used Online TurboTax, you can check by looking at the Tax Home in your Online account.
Or did you choose to file by mail instead? TurboTax does not mail it for you. If you chose that method, you have to print, sign, date, and mail it.
The FAQ below tells how to check on a state refund. When you scroll down further there, you will see a link for your state to get to its refund lookup tool. Some state revenue department websites have a FAQ section or info on their refund lookup page that tells about how long it takes in that particular state.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...
After checking all of the above, if your processing is taking longer than the usual time frame for your state, you can phone your state department of revenue's customer service to see if they can tell you the reason for the delay.
FAQ: How do I contact my state's department of revenue?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-rev...
