Rich Hill Township is one of the twenty-five townships of Muskingum County, Ohio, United States.Located on the eastern edge of the county, it borders the following townships: No municipalities are located in Rich Hill Township.Rich Hill Township was established in 1815.[5] The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.There is also an elected township fiscal officer,[6] who serves a four-year term beginning on April 1 of the year after the election, which is held in November of the year before the presidential election.