Green Hill is a small unincorporated community in Medina Township, Warren County, in the U.S. state of Indiana. The town was platted on March 5, 1832 by William B. Bailey and his brother Horatio who named it Milford, for their home town of Milford, Delaware. The plat included 48 lots, two north/south streets and three east/west streets. The first store op…Green Hill is a small unincorporated community in Medina Township, Warren County, in the U.S. state of Indiana. The town was platted on March 5, 1832 by William B. Bailey and his brother Horatio who named it Milford, for their home town of Milford, Delaware. The plat included 48 lots, two north/south streets and three east/west streets. The first store opened in 1833 and was followed in subsequent years by several more businesses, including a liquor store, blacksmith, grocery, tannery, shoe-maker, wagon-maker and others. A post office was established on December 2, 1837 as Poolesville, in honor of the town's first resident physician, Dr. Poole — it retained the name until August 13, 1904.