Ms. Ortega, who the police said was a naturalized American citizen from the Dominican Republic, had worked for the Krims for about two years. She had been referred by another family, the police said, and did not come through an agency, which customarily does background checks. A law enforcement official said Ms. Ortega had had no previous brushes with the law, nor have detectives learned of any tensions in her relationship with the Krims.

Image Yoselyn Ortega

“No fighting with the mom, the family, the kids,” the official said. “Everybody is looking for a reason here.” He added, “We’ve got nothing bad other than the fact that she killed two children.”

On Friday, the sort of memorial with stuffed animals and flowers that has become sadly familiar in the aftermath of a city tragedy took shape outside the Krim apartment building, as parents pondered what to say to their own children. Disbelief was pervasive in the neighborhood.

“I don’t have words for something like that,” said William Davila, whose daughter is a fifth grader at Public School 87, which Lucia Krim, 6, had attended. The children’s father, Kevin Krim, was returning from a business trip on Thursday when he was met by the police at the airport.

Mr. Krim learned that his youngest child, Leo, and his daughter Lucia, known as Lulu, had died and that the police had arrested the nanny with whom the Krims were so close that they had traveled to her home in the Dominican Republic. He is an executive at CNBC. Ms. Krim did not work outside the home, but taught an occasional art class at the Museum of Natural History. On Thursday night, CNBC put the Krims up in a hotel.

Mr. Krim’s father, William Krim, 74, said the parents had not returned to their apartment.

“I don’t know if they ever will,” he said. “I don’t know if I could.”

A spokeswoman for the Office of the Chief Medical Examiner, Dr. Charles S. Hirsch, said Lucia had died of “multiple stab and incise wounds,” and Leo of “incise wounds of the neck.” They had been clothed, a law enforcement official said, suggesting that Ms. Ortega had not been bathing the children.