Holmes asked the question in a video played for jurors Monday, which showed two detectives interviewing him at the Aurora Police Department about two hours after the July 2012 attack, which killed 12 people and injured 70 others.
Det. Chuck Mehl testified later that Holmes had seen a sign in the police department that said "Crimes Against Children Unit," which might have prompted the question.
Detectives didn't answer Holmes' question directly but said, "We'll get to that."
Holmes pleaded not guilty by reason of insanity to 166 counts including murder and attempted murder. His attorneys acknowledge he was the shooter but say schizophrenia had so distorted his mind that he could not tell right from wrong.
Prosecutors say Holmes was sane and are asking jurors to convict him and sentence him to death.
In the video, Holmes is wearing a torn shirt, undershorts and fiery orange hair. His voice is thick and groggy.
Asked if he needs anything, he says, "Oxygen." The detectives ask if he is having trouble breathing or wants a fan, but he says no.
When asked how to spell "Holmes," he answers, "Like Sherlock."
Mehl testified that Holmes at one point pulled an empty paper cup to the edge of the table where he was sitting and tried to flip it onto a water bottle, like game of ring toss. That wasn't on the clip shown in the courtroom.
A brief clip of Holmes in the interview room had been played for jurors during opening statements on April 27, but this was the first time his conversation with the detectives was shown in court.
Mehl offered no explanation for Holmes' behaviour, and neither side asked him about it.
Earlier Monday, a volunteer supervisor at a gun range testified that a man with bright orange hair who showed up at the facility in the summer of 2012 was such an odd sight that he and another supervisor went to talk to him.
The volunteer, Theodore Maples Jr., didn't say who the man was, but the reddish-orange hair and weapons he fired matched descriptions of Holmes and his arsenal.
"That really flagged us," Maples said of the man's hair.
Judge Carlos A. Samour Jr. didn't allow Maples to recount the conversation after the defence objected to a prosecution question about what was said.