Leonardsville Township was organized in 1881, and named for Patrick Leonard, an early settler.

[3] According to the United States Census Bureau, the township has a total area of 38.5 square miles (100 km2), all land.

There were 54 housing units at an average density of 1.4 per square mile (0.54/km2).

16.7% of all households were made up of individuals, and 6.3% had someone living alone who was 65 years of age or older.

There were 19.4% of families and 17.2% of the population living below the poverty line, including 10.0% of under eighteens and 11.4% of those over 64.