Police said a patrol went to 247 Branford Street, described as a quiet and safe neighborhood, at about 3:45 p.m. on Sunday after ShotSpotter, the gunfire detection system, was activated and recording 11 rounds fired.
The little girl was hit in the face while inside the home.
Police said they found the girl's father putting her in a car and she was driven to St. Francis Hospital but was later taken to Connecticut Children's Medical Center.
Police on the scene said they found five spent bullet casings and saw bullet holes in the house. Glass was also shattered from windows.
A witness told police that the shots came from a black car that was heading east, but police do not have any suspects.
Police say that it was not a drive-by shooting, and the neighbors aren't in any danger.
Nobody else was injured and there haven't been any arrests yet.