I have to disagree with SD Realtor. When lenders require it (which is almost always) escrow does pay property taxes when escrows close and property taxes are due. 1st installments are due 11/1 and delinquent if not paid by 12/10, 2nd installments are due 2/1, delinquent if not paid before 4/10. They lien on the due dates. So most months, taxes will not be paid, only prorated, but if they are upaid from 11/1 to 12/10 and 2/1 to 4/10 they will be paid directly from escrow.
So if you close after 2/1 but before 4/10, and property taxes haven’t been paid, escrow will pay it, but from the sellers funds, not yours. (At least that’s usually the way they do it, because it will technically have liened against the seller.) You will have a precise prorate of the actual tax bill which is due on 4/10.
Between July 1 and November 1, taxes may be estimated because they have not yet liened, and the precise amount may not be known (though the estimates are usually pretty good.) That estimate will be based on the previous assessed value. If the new assessed value is less, you’ll get a refund and a negative supplemental tax bill.