Kinjal Patel, 27, the Indian-origin babysitter, has already been charged in the case with manslaughter in the first degree and is being held on a USD 1 million bond.
She allegedly told police that she became angry with the child and forced him to the floor, where he hit his head. The incident occurred at her home in New Haven on January 16.
The baby's mother, Thenmozhi Rajendran, 24, and his father, 33, Mani Sivakumar, both of 77, have been charged with risk of injury to a child and interfering with police.
Police responded to a "risk of injury" complaint at Yale-New Haven Hospital Paediatric Emergency Department and found the boy's skull was "severely fractured".
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As the boy, Athiyan Sivakumar, was rushed to surgery, doctors told police his injuries were life-threatening.
The boy died on Sunday from his injuries. The Office of the State's Chief Medical Examiner determined his death was "homicide caused by blunt force".
On Wednesday, detectives interviewed Patel, who said she called the child's father to tell him his boy was injured. He came home and took his son to a hospital.