Falls Township consists of two disconnected portions in the center and northeast of the county, separated by a short distance.

While many Ohio townships are composed of disjointed pieces due to municipal annexations, separation only by other townships is very uncommon.

Its northeastern portion (known as The Gore, or simply Gore) borders the following townships: Its southwestern portion borders the following townships: The majority of the city of Logan, the county seat of Hocking County, is located in the southwestern portion of Falls Township.

[4] Statewide, the only other Falls Township is located in Muskingum County.

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.