State tax withholdings should show up on your state return to be applied toward your state income tax.
There is also a Tax Payments worksheet that is included as part of your Federal return where the state withholdings will also be shown. This is not a form that is filed with your return. It is just in the background of some of the calculations.
If you are using a desktop version of TurboTax, you can click Forms at the top of the screen to see the Tax Payments worksheet. If you are using TurboTax Online, then the Tax Payments worksheet may be selected for printing after your TurboTax fee has been paid.