Holmes is accused of killing 12 people and injuring 58 in a shooting rampage during a Friday premiere of "The Dark Knight Rises," in Denver.
According to investigators, Holmes has so far refused to cooperate with the police.
Colorado authorities are expected to file formal charges against him on July 30. He is expected to remain in jail until his next court date.
US media said that according to police sources Holmes has shown no remorse for his actions, and told them that he was the "Joker" character from the Batman movie series.
Legal experts said that Holmes' attorneys may use an insanity plea in order to spare him from a capital punishment sentence.
The State of Colorado reinstated the death penalty in 1976, but exercising it has been rare. There has been only one execution in Colorado in the past 30years, that of Gary Lee Davis, who was executed by lethal injection in October 1997.
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