James Holmes faces charges in the July 20 shooting that left 12 dead and 58 others wounded.
Holmes was a promising neuroscience doctoral candidate, but by the end of the programme's first year, he had fallen out of favour with professors besides failing a key exam, prosecutors said.
"What's going on in the defendant's life at the time is extremely relevant to this case," Chicago Sun-Times quoted Chief Deputy District Attorney Karen Pearson of their need for relevant documents.
Holmes' defence lawyer, Daniel King, has said Holmes is mentally ill, setting up a possible insanity defence. But Pearson's arguments on Thursday revealed a possible motive: Holmes' anger that he was failing at school, "at the same time he's buying an enormous amount of ammunition, body armour and explosives."
Details of his behavior before he became a suspect in a suburban Denver theater shooting were not released. But it raised enough concerns for campus police to run a background check on Holmes, although University of Colorado spokeswoman Jacque Montgomery declined to elaborate on the reason.
Prosecutors argued that gaining access to the school records would establish a motive by showing what Holmes hoped to accomplish at CU and the "dissatisfaction with what occurred in his life that led to this."
Pearson said that professors had sought to keep Holmes out of their labs and that "professors urged that he find another line of business."
University officials said Holmes lost access to university buildings after his withdrawal because his student access card was shut off, not because of threats.
The dive in Holmes' academic performance could be a possible motive, one legal observer said.
"That's the kind of thing that is classic motivation for a murderer and doesn't support insanity," said Craig Silverman, a criminal defense attorney and former Denver prosecutor.
