As of the 2020 census, 2,090 people lived in the township.

Located in the southeastern corner of the county, it borders the following townships: Part of the village of Oak Hill is located in western Madison Township.

[4] It is one of twenty Madison Townships statewide.

[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.