There are 15 US Post Offices in Butler County serving a total of 294,757 residents equating to 19,650 residents per post office. It's estimated that approximately 470,465 packages are handled across the 15 county post offices annually. Butler County is a county located in the U.S. state of Ohio. As of the 2010 census, the population was 368,130. Its county seat is Hamilton. It is named for General Richard Butler, who died in 1791 during St. Clair's Defeat. It is also home to Miami University, an Ohio public university. Butler County is part of the Cincinnati, OH-KY-IN Metropolitan Statistical Area."