There are 9 US Post Offices in Greene County serving a total of 32,510 residents equating to 3,612 residents per post office. It's estimated that approximately 51,890 packages are handled across the 9 county post offices annually. Greene County is a county in the U.S. state of Indiana. As of 2010, the population was 33,165. The county seat is Bloomfield. The county was determined by the U.S. Census Bureau to include the mean center of U.S. population in 1930. Greene County is part of the Bloomington, Indiana, Metropolitan Statistical Area.