Yes. Property taxes are prorated on a fiscal year July 1st - June 30th that's divided into 2 installments, July 1st - December 31 and January 1st to June 30th.
For example, If Seller had already paid until December 31st and Buyer closed sale on September 1st, then Seller is due a refund for the remaining months and days until December 31st from the closing date.
Your escrow officer could better explain you this.
Also, prepare to pay additional Supplemental Taxes after closing.
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