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 $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, Mani Sivakumar, 33, have been charged with risk of injury to a child and interfering with police.
They turned themselves in at police headquarters, The Hartford Courant newspaper reported on Thursday.
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".
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.
The toddler after the injury began to cry and convulse.
The father returned home and brought the baby to the hospital, police said adding that they were also called to the hospital where doctors told them that the boy's injuries were life-threatening.
The family's home was immediately secured as a potential crime scene, police said.
Officers said they were dispatched to the child's home as the boy went into surgery. They said they secured the home as a potential crime scene.
Police said the boy died from internal bleeding and a skull fracture on January 19.
The Chief Medical Examiner concluded that the death was a homicide caused by blunt force.
"Any homicide is a tragedy," said Chief Dean Esserman of the New Haven Police Department.
"None, however, is more tragic than that of an innocent young child. His death was senseless and has affected us deeply."
Authorities interviewed Patel on January 22 and she admitted to them that she was babysitting the boy. According to court records, Patel first told the police that the boy woke up convulsing.
She then changed her story to say that the boy had slipped on the wet kitchen floor. She later called the police again and said she wanted to tell the truth.
In a follow-up interview, Patel told them she became angry and demonstrated how she grabbed the boy and violently slammed his feet up and down on the kitchen floor approximately three times.
She said she then grabbed the boy's cheeks and forcefully shook his head back and forth. She told the police that she pushed the victim's face and he fell backwards, hitting his head on the kitchen floor.
Patel told police she did it because the child was spitting food and water at her.
In court records, she was quoted as saying to the baby, "Why don't you listen to me? I am the one who is always watching you."
Patel said the child began to cry and convulse. She then phoned the child's father, who took the boy to hospital, according to detectives.
A woman, who lived in a house below the couple's, told police that she heard a loud banging coming from the couple's home on January 16.
Police said they believe that banging was the sound of the crime in progress.
Patel's public defender told Eyewitness News she was very afraid and was seen trembling in court.
Image: Kinjan Patel (right), baby’s mother Thenmozhi Rajendran (centre) and Mani Sivakumar
Photograph Courtesy: New Haven Police Department