Some states (like MO, CO, LA, WV, GA, etc.) can take a long time processing returns--even several weeks--as they crack down on detecting fraudulent returns.
You need to first check to be sure that your state return was successfully filed.
If you efiled, what do you see when you check with this tool? Was your state return accepted?https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp
If that showed your efiled state return was accepted, or if you printed and mailed the return, the FAQ below tells how to check on a state refund.
TIP: While you're at your state's tax website, also look for a statement or FAQ that may say about how long it takes to get a refund in your state and how to long to wait before phoning them.
FAQ: How do I track my state refund?