First, 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? If so, 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, and you'll see a link to get to your state's refund lookup tool. Some states take a long time to process a refund. If you think it's been too long for your state, you can phone your state's department of revenue to see if they can give you any info.
Choose your state from the chart below the video in this FAQ:
FAQ: How do I track my state refund?
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571