Some of the following you've already done. But here's a full answer for completeness and for others.
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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:
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 and has a link for your state. Then you'll see information for your state (which may include info on how long it takes in your state) and a link to go to your state's "Where's My Refund" tool. Your state may also have a FAQ section at it's "Where's My Refund" site that tells how long to expect in your state.
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