Some states are fairly quick with refunds, while other states can take a long time processing returns--even several weeks--as they crack down on detecting fraudulent returns. Here are some things you should check:
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.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...