The tax statement can be forwarded to the new owners, or return the statement to the County Treasurer with a note indicating ownership has changed.
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 the taxes were handled should be on the settlement statement provided at the closing time of your real estate transaction. Contact the realtor or the attorney who handled the transaction to confirm.
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.