There are 1 US Post Offices in Robertson County serving a total of 2,073 residents equating to 2,073 residents per post office. It's estimated that approximately 3,309 packages are handled across the 1 county post offices annually. Robertson County is a county located in the U.S. Commonwealth of Kentucky. As of the 2010 census, the population was 2,282. Its county seat is Mount Olivet, Kentucky. The county is named for George Robertson, a Kentucky Congressman from 1817 to 1821. Robertson is a prohibition or dry county. It is the smallest county by both population and total area in Kentucky."