Madison Township is centered at 40°47'22" North, 82°28'36" West (40.789444, -82.476666).[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.Madison Local Schools enroll 3,218 students as of 2012–2013.The adult education facility is located at Madison Comprehensive High School.Law enforcement in Madison Township is the responsibility of the Richland County Sheriff's Office,[8] and fire protection and ambulance services are provided by the Madison Township Fire Department.