The suspect, who was arrested following the attacks which killed 12 at the Century 16 Theatre, told officers he had explosives in his car and home.
He has been identified as a former student from University of Colorado Medical School.
A bomb disposal squad is currently examining a Hyundai in the cinema's car park for explosive devices and a nearby apartment block has been evacuated and surrounded by SWAT teams.
"The suspect who is in custody made a reference to explosives at his residence, so police have evacuated a building in North Aurora," Aurora police chief Dan Oates told the media.
Reading out a statement on the Holmes family's behalf, Lieutenant Andra Brown of the SD Police Department, said: "Our hearts go out to those who were involved in this tragedy."
"We ask that the media respect our privacy at this difficult time... We are still trying to process this info and appreciate that people respect out privacy."