It depends on what state. 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 the state return, and it was accepted, or if you mailed the state return, 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 table in this FAQ for more info:
FAQ: How do I track my state refund?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...
