Police found 16-year-old Deontae Boykin, shot, in the living room of a house on Connecticut Avenue, just before midnight on Friday night.
Police say the victim was alert when police arrived and told them he was shot while he looked out the window after hearing arguing outside.
Detectives found what appeared to be a bullet hole in the window.
Boykin is listed in critical but stable condition at Yale-New Haven Hospital.
Police continue to search for a suspect, but did recover a gun in a nearby yard.