How do I enter out of state purchases to pay sales and use tax on Ky return

To enter out-of-state purchases on the Kentucky return for the Use Tax, go to the Kentucky state interview in TurboTax.

Proceed (a long way) through the interview until you encounter a screen with the heading "Out-of-State Purchases or Services". Answer "yes", then answer the subsequent questions about the size of the purchases.

NOTE: this screen will not appear if you are filing a non-resident Kentucky return.