The amount of your State refund should show up on the left hand side of the page when you first log back into your account / return.
Look at StevenC1's answer. If that does not help because TurboTax won't let you get there, try clicking the button to add a state. No, you're not really going to add a state, but TurboTax will let you in so that you can see your whole return. When you are finished, close without saving.
Note that this is a very good reason for you to save a copy of the PDF file generated by TurboTax - you should always keep a copy of all tax documents that you file.
How do I find out the amount of my state tax refund?