Did you physically print, sign, date, and mail the state return yourself? TurboTax does not mail it for you.
Did you also file the Federal return by mail? If so, then, hopefully, you didn't mail both returns in the same envelope to the IRS. They go in separate envelopes to separate places.
When sending things to tax agencies it's a good idea to mail by a method that has tracking such as certified return receipt, priority mail, etc.
If it's not showing up in your state's "Where's My Refund" tool, then you can phone the state tax agency and ask them to look it up.
FAQ: How do I track my state refund?
