Located in the northern part of the county, it borders the following townships: No municipalities are located in Madison Township.

It is one of twenty Madison Townships statewide.

[4] In 1833, Madison Township had one saw mill, one flouring mill, one salt factory, one physician, one attorney, and several ancient mounds.

[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.