Greenwood City Hall is located at 2 North Madison Avenue, Greenwood, IN 46142.
Originally known as Smocktown, for brothers John and Isaac Smock who settled here with their families about 1823. A post office was established in 1825 with James Smock serving as postmaster and also, the first justice of the peace. The town's name was changed to Greenfield in 1825 and again, in 1833 to Greenwood to avoid confusion with the nearby Hancock County town of Greenfield. Greenwood was incorporated as a town in 1864.