Before the child died, her parents were arrested on abuse charges, but now they could face more serious charges. Officials said yesterday that a grand jury would begin this week to weigh charges against her parents in the death.

The girl's mother initially told detectives that the child was not hers and that she had recently been smuggled into the United States from Mexico, where she suffered the injuries, the police said. But the mother has since admitted that she withheld food from the girl, Edith Gonzalez, as punishment, a senior law enforcement official said.

The woman, who also gave the police a false name and address when she was arrested late Monday, was arraigned yesterday on charges of endangering the welfare of a child, a felony, and reckless endangerment, a misdemeanor. Her boyfriend, the child's father, was arrested late Tuesday and arraigned yesterday on the same charges. Both pleaded not guilty and were held without bail.

At the two arraignments yesterday, in Brooklyn Criminal Court, and in interviews with investigators and neighbors, a picture began to emerge of a household where abuse of the little girl seemed more the rule rather than the exception.

Punishment, as the child's mother and father put it in statements to the police and prosecutors, was not limited to withholding food and beatings— he said he beat her with his fists, a belt and a cable and that the child's mother struck the three-year-old with a cable, according to court papers and the law enforcement official. The mother also admitted that she sometimes plunged the child into a tub filled with ice water, the official said.

The mother, now identified as Tania Cabrera, 23, first told the police that her name was Patricia Aguirre and that she was 25 years old.

Ms. Cabrera, in her statements to the police and prosecutors, detailed instances of abuse in the home that the couple share on George Street in Bushwick, Brooklyn, with their daughter and Ms. Cabrera's five-year-old boy with another man, the official said. She said her boyfriend, Edison Gonzalez, 19, favored Edith over the boy, Javier, prompting arguments, and Ms. Cabrera said she eventually took out her frustration on the girl, the official said. Ms. Cabrera also said Mr. Gonzalez would drink and become abusive.

It remained unclear yesterday exactly how the little girl suffered the skull fracture and cerebral bruising that were among her most serious injuries, but the criminal complaints charging Ms. Cabrera said that the child had seizures on both Sunday and Monday, and that on the second day, the child fell from a chair, striking her head.

An autopsy to determine the cause of death, which will in some measure determine whether more serious charges are brought, will be performed today, officials said.

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