But it remained unclear what prompted him to turn his rage on his cousin’s wife, Ms. Li, 37, and their four children, identified by the police as Linda Zhuo, 9; Amy Zhuo, 7; Kevin; and William Zhuo, 1.

The police said Mr. Chen appeared to have stayed with them before without incident. The family did not appear to be better-off than those who lived around them in their Chinese enclave near Ninth Avenue in Brooklyn, neighbors said. They sent their three school-age children to a local public school, the Education Department said. Ms. Li stayed at home with William. The authorities had no record of troubles in the household.

May Chee, who is a neighbor of the family and grew up on the block, said she would often see Ms. Li outside with her children, who would chase one another and play with the other children who live along 57th Street, a block teeming with young people.

Ms. Li watched over them from her front stoop, often chatting on her cellphone, said Ms. Chee, who added that the mother did not speak much English.

Few in the area recalled Mr. Chen, who had only recently arrived there.

A woman who lives next to the family and gave her name only as Ms. Zheng said she had seen the cousin in recent days standing outside the two-story, two-family home, smoking cigarettes and talking on the phone.

A cousin of the mother, Yun Gao, 29, told reporters near the home on Sunday that Mr. Chen was emotionally unstable; she did not elaborate.