Located in the southern part of the county, it borders the following townships: The village of Arlington is located in northern Madison Township, and the unincorporated community of Williamstown lies in the southern part of the township.It is one of twenty Madison Townships statewide.It was named for James Madison, fourth President of the United States.[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.