The FAQ below will give you some info on that.
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.
See the info in this FAQ:
FAQ: How do I track my Ohio state refund?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-ohio-tax-refund/L5PR7qz...