Because Thaiya’s death is the subject of a criminal investigation, there will be an autopsy.

Mr. Smith, 26, and Ms. Spruill, who turns 25 on Monday, have known each other since grade school, Ms. Spruill said. In Ms. Spruill’s telling, Mr. Smith ran with a rough crowd and had little interest in Thaiya until Ms. Spruill married Mr. Adams last spring. In Mr. Smith’s telling, he was a doting father who fought continually for custody of his daughter, complaining to officials this summer that he feared she was being abused.

It was messy. In September, the city’s children’s protection agency moved Thaiya to the home of Diane Howard, Ms. Spruill’s grandmother, for four days while investigating abuse allegations. Thaiya was then returned home.

In October, Mr. Smith said, he was arrested after keeping Thaiya at his mother’s house in Red Hook for two weeks, saying she cried because she didn’t want to go back home. Ms. Spruill said she got an order of protection against Mr. Smith because he threatened to kill her. The case worked its way through Family Court, Mr. Smith said.

Meanwhile, Thaiya stayed with her mother and stepfather, in a one-bedroom apartment in the Tilden Houses in Brownsville.

On Wednesday morning, Thaiya ate Froot Loops and some yogurt. She watched “Space Jam.” Ms. Spruill, who said she was put on bed rest because of a complicated pregnancy, got ready to go to the housing office at the Tilden Houses to request a transfer to another housing project, where Mr. Smith would not know where to find her.

Thaiya started crying, because she wanted to go with her mom. But Thaiya could not walk that fast, and Mr. Adams was home. As Ms. Spruill left, Thaiya was still crying.

Ms. Spruill said she was gone for less than an hour. When she returned, she checked on her daughter, sleeping in the bedroom. Hours later, Thaiya got up, Ms. Spruill said. She was talking. Yes, she wanted some apple juice. No, she did not want any broccoli.