I’m selling my property and closing is in a few days. Do I still have to pay the tax bill I received?

If your closing is after the due date of the property taxes, you should pay the property taxes and inform your lawyer of the payment so that your lawyer can reflect it on the Statement of Adjustments. 

You should not worry about overpayment as by reflecting the payment in the Statement of Adjustments, your lawyer will make sure that you only pay up until the closing date.