After you file

The state tax payments would be an itemized deduction on the Federal return.

These payments can be entered as follows:

To enter estimated taxes paid (Federal, State, Local)
•    Click on Federal Taxes (Personal using Home and Business)
•    Click on Deductions and Credits
•    Click on I'll choose what I work on (if shown)
•    Scroll down to Estimates and Other Taxes Paid
•    On Other Income Taxes Paid, click on the start or update button