Colorado does have the authority to kill for certain criminal offenses, but the prosecution would never win the case. His recent behaviour even before the event points to insanity. If the jury were to decide guilty, the defense would push for a mistrial, since no one in the vicinity is not already predisposed to find him guilty. The trial would need to be outside of Colorado for an unbiased verdict.
Colorado does have the death penalty. It was reinstated back in January 1st of 1975 after a ruling that declared it unconstitutional 3 year earlier. James Holmes will probably get the death penalty for what he did but that's only if he is sane. You can read all about it at http://en.wikipedia.org/wiki/Capital_punishment_in_Colorado.
By all that is right in this world the police should have put 2 in his head immediately. Now his attorneys will get him placed into the nut hut & we'll pay to keep him alive for 60 or 70 years. He's got a 1 way ticket to hell & his trip needs to be expedited