Police said 15-year-old Tyler Giuliano was shot at about 1 a.m. Thursday in New Fairfield, a town along the New York line just north of Danbury.
A woman who was alone in the house believed someone was breaking in and called the teen's father, who lives next door, and he grabbed a gun and went outside to investigate, police said.
The father confronted someone wearing a black ski mask and black clothing and then fired his gun when the person went at him with a shiny weapon in his hand, police said.
When police officers arrived, the teen was lying in the driveway of the woman's home with gunshot wounds and the father was sitting on the grass. The teen was pronounced dead at the scene, police said.
"All in all it's a tragedy," state police spokesman Lt. J. Paul Vance said.
The teen's father, Jeffrey Giuliano, a fifth-grade teacher in town, hasn't returned a message seeking comment on what happened.
The teenager was a student at New Fairfield High School, a short walk from the neighborhood where he was killed.
Superintendent of Schools Alicia Roy sent parents an email about what happened, The News-Times of Danbury reported.
"Our district has experienced a tragedy that has affected us deeply," she wrote, adding that students weren't told of the killing because all the facts weren't clear.
No charges have been filed. State police are investigating. An autopsy on the boy is planned.