In a typical real estate transaction, taxes are prorated and the buyer is either given credit for the seller's portion or the seller pays the taxes directly to the County Treasurer as part of the property sale. Details of how your taxes were handled should be on the settlement statement provided to you at the closing of your real estate transaction. You can also review this with your realtor or the attorney who handled the transaction for you.
Real estate taxes are always a year behind. For instance: the taxes due in September and March cover the time period from July 1 – June 30 of the previous year.