Bridgeport High School was constructed in 1881 on a hilltop location between Congress and Arch streets.. It was "far removed from all the noise, dust, or odors arising from factories, stables or the like..." according to a newspaper account of the time.
It was replaced by a new building across the street on Lyon Terrace in 1916, on top of Golden Hill (the site of the present day City Hall). To the north of the hill was the "Hollow" section of Bridgeport. To the south was a 100 foot drop to Fairfield Avenue. To the east was Main Street and the old downtown area. To the West was a long drop down to Park Avenue.
In the first edition of the school newspaper, "The Criterion" on October 18, 1918, one of the headlines read "HILLTOP BOYS TO TACKLE FAST NEW HAVEN SQUAD". So the nickname Hilltop has been around at least since then.
When Central moved to its new location in 1964 it brought its Hilltopper nickname with it. Sometime after that a ram, which lives on hill tops was added to many of the sports logos.