You must prorate. You can only deduct the portion of the property tax that corresponds to your period of ownership. Since you did not become the owner until August, you can only deduct the portion of the property tax that applies to the time period from the August closing date forward.
The deduction for the portion that occurred prior to the closing date belongs to the seller, even though you may have actually paid the entire year's amount. That is why the seller provided you with a credit.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
