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According to the United States Census Bureau, the township has a total area of 67.7 km² (26.1 mi²). 67.7 km² (26.1 mi²) of it is land and none of the area is covered with water.
Adjacent places are: West Perry Township, Chapman Township, Franklin Township, Washington Township, and Juniata County.
Perry Township was founded in 1816.
As of the census of 2000, there are 1,973 people, 686 households, and 539 families residing in the township. The population density is 29.1/km² (75.5/mi²). There are 729 housing units at an average density of 10.8/km² (27.9/mi²). The racial makeup of the township is 99.24% White, 0.05% African American, 0.00% Native American, 0.10% Asian, 0.00% Pacific Islander, 0.05% from other races, and 0.56% from two or more races. 0.41% of the population are Hispanic or Latino of any race.
There are 686 households out of which 36.2% have children under the age of 18 living with them, 68.7% are married couples living together, 5.8% have a female householder with no husband present, and 21.4% are non-families. 18.8% of all households are made up of individuals and 7.9% have someone living alone who is 65 years of age or older. The average household size is 2.88 and the average family size is 3.28.
In the township the population is spread out with 29.5% under the age of 18, 8.1% from 18 to 24, 29.0% from 25 to 44, 23.0% from 45 to 64, and 10.4% who are 65 years of age or older. The median age is 34 years. For every 100 females there are 105.1 males. For every 100 females age 18 and over, there are 99.7 males.
The median income for a household in the township is $35,167, and the median income for a family is $40,474. Males have a median income of $28,808 versus $21,667 for females. The per capita income for the township is $14,631. 12.1% of the population and 7.3% of families are below the poverty line. Out of the total people living in poverty, 17.9% are under the age of 18 and 10.7% are 65 or older.