You need to read IRS Pub 530 at
Publication 530 (2013), Tax Information for Homeowners
where it says:
"
Real estate taxes paid at settlement or closing. Real estate taxes are generally divided so that you and the seller each pay taxes for the part of the property tax year you owned the home. Your share of these taxes is fully deductible if you itemize your deductions.
Division of real estate taxes. For federal income tax purposes, the seller is treated as paying the property taxes up to, but not including, the date of sale. You (the buyer) are treated as paying the taxes beginning with the date of sale. This applies regardless of the lien dates under local law. Generally, this information is included on the settlement statement you get at closing. You and the seller each are considered to have paid your own share of the taxes, even if one or the other paid the entire amount. You each can deduct your own share, if you itemize deductions, for the year the property is sold.
Example.
You bought your home on September 1. The property tax year (the period to which the tax relates) in your area is the calendar year. The tax for the year was $730 and was due and paid by the seller on August 15.
You owned your new home during the property tax year for 122 days (September 1 to December 31, including your date of purchase). You figure your deduction for real estate taxes on your home as follows.
1. Enter the total real estate taxes for the real property tax year = $730
2. Enter the number of days in the property tax year that you owned the property = 122
3. Divide line 2 by 365 = .3342
4. Multiply line 1 by line 3. This is your deduction. Enter it on Schedule A (Form 1040), line 6 = $244
You can deduct $244 on your return for the year if you itemize your deductions. You are considered to have paid this amount and can deduct it on your return even if, under the contract, you did not have to reimburse the seller."
You will notice that the example does not care what the actual amounts were on your closing settlement documents. You take credit for the pro-ration of the actual amount billed for the year.