There are 2 US Post Offices in Finney County serving a total of 36,387 residents equating to 18,194 residents per post office. It's estimated that approximately 58,078 packages are handled across the 2 county post offices annually. Finney County (county code FI) is a county located in the U.S. state of Kansas. As of the 2010 census, the county population was 36,776. Its county seat and most populous city is Garden City.