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

Antrim is an unincorporated hamlet in the township at the junction of US 22 and SR 513[4] and was the site of several former schools.

[7] A school named Madison College operated from 1835 through 1859.

[8][9] 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,[10] 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.