Posey Township is one of twelve townships in Rush County, Indiana. As of the 2020 census, its population was 1,078 and it contained 451 housing units.
The Offutt Covered Bridge was listed on the National Register of Historic Places in 1983.
According to the 2010 census, the township has a total area of , of which (or 99.94%) is land and (or 0.06%) is water.
(This list is based on USGS data and may include former settlements.)