There are 6 US Post Offices in Grayson County serving a total of 28,072 residents equating to 4,679 residents per post office. It's estimated that approximately 44,806 packages are handled across the 6 county post offices annually. Grayson County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 25,746. Its county seat is Leitchfield. The county was formed in 1810 and named for William Grayson (1740-1790), a Revolutionary War colonel and a prominent Virginia political figure. It is a prohibition or dry county, though a bill was passed on March 23, 2010 to allow limited alcohol sales in restaurants."