After you file

1099-G can be used for any government payment, so I am not sure why your 1099-G was issued.  Is it perhaps a KY State Refund?

If you itemized last year (2016) and claimed a deduction for State Income Tax you will need to complete this section.

If you claimed the standard deduction  for 2016 you do not need to report your 1099-G for State Tax Refund.

Many people do not understand this question:"Total of all your payments and withholding"

You'll find most of this info on your 2016 state tax return.

This is the total amount of everything you paid into the State for 2016 including:

 - Amounts withheld on your W-2, W-2G, and 1099

 - Estimated tax payments for 2016. Add any paid in 2017 for 2016 (it's common for the 4th quarterly payment to be made in January)

 - Overpayment from 2015 applied toward your 2016 return

 - Payment made with an extension of time to file

 - Payment made when you filed your return

 - Refundable credits

I recommend looking at your Kentucky tax return for TOTAL PAYMENTS line.  This is what you input into this screen.