I filed an extension on the Georgia site and they have an option to make a payment if you owe tax. I opted to make a payment through ACH, so the money came out of my checking account. It went to the Georgia Dept of Revenue, Georgia Tax Center. I received a confirmation from the state and my checking account shows the withdrawal. This is state only. I made a separate payment to the US IRS.
The state letter lists 22 line items from my return. One column lists my numbers. The second column shows the state's computations. All the numbers match except for Estimated Tax Paid where my return shows $2072 and their column shows $0. The letter says for me to submit documentation that I have paid the estimated tax.
