You didn't name the state, but the FAQ I've provided at the end of this message will show the lookup tools for all the states. So pick your state there.
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.
If you successfully filed, then 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.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...