Jurors were told proceedings would resume Wednesday, KSTU, Salt Lake City, reported.
Brian David Mitchell, 57, is charged with kidnapping Smart, then 14, in 2002, and holding her for nine months as a second wife. Smart was found in March 2003 in Sandy, Utah, with Mitchell and his wife, Wanda Barzee.
Mitchell sang the Christmas carol "O Holy Night" as he was led into the courtroom Tuesday. But he screamed and fell down as the judge spoke to jurors.
His stepdaughter, Rebecca Woodridge, told KSTU Mitchell has had seizures recently.
"I don't think there's any reason for him to fake this," she said.
Mitchell's lawyers say he is insane. Gregory Porter, a therapist at the Utah State Hospital who testified Monday, was the first of what is expected to be a series of witnesses on Mitchell's mental competency.
Porter described Mitchell as someone who was "pragmatic," able to get what he wanted even when he was not talking by using notes and signing them with his legal name as well as the religious one he uses, Immanuel David Isaiah. Porter said Mitchell is "delusional" but described the delusions as "encapsulated" so that he has "islands of health."