Dr. First said it was “a possibility.” Yet, Dr. First added, “he could also be imagining or making up the fact that he strangled Etan Patz.”

Dr. First said he had ruled out the possibility Mr. Hernandez was malingering in part because Mr. Hernandez had shown signs of the disorder before his arrest in 2012.

Carmen Foschini, a younger sister of Mr. Hernandez’s, testified that out of 12 siblings, she was the closest to Mr. Hernandez in childhood. She said he was protective and caring. “He was a good brother,” she said, adding, “He was always there for us.”

He did not appear to have many friends, she said, except for a boy who lived near them and who, years later, was one of the people to whom Mr. Hernandez confided that he had killed a child. But, she conceded, the friend had a crush on her, and that could have been the reason he was often around.

Prosecutors argued Mr. Hernandez’s lack of friends could have been a reflection not of a personality disorder but of a strict and abusive father who kept his children from playing team sports or bringing friends home.

Ms. Hernandez described seeing Mr. Hernandez having a conversation, even moving his hands, although no one was with him, and she recalled hearing him screaming loudly in his sleep. But he tried to keep these experiences to himself, she said.

“He doesn’t like to tell us,” she said, “because he doesn’t want to scare us.”

At various moments during her testimony, when she recalled him struggling, and failing, to assemble a desk and an entertainment center, Mr. Hernandez was slumped in his chair and looking down. Ms. Hernandez also said that she had found cocaine belonging to him in the family’s car.