You don't sue over the commission of a crime. You sue over a civil offense. So the fact that it's not a crime is totally irrelevant. However, the only person who seems likely to be considered civilly liable is James Holmes, and suing him would be pretty pointless, since I'm pretty sure he is the proverbial turnip from which you can't squeeze blood.
Here is an article from the
Denver Post that includes commentary from DU Law Professor Tom Russell (who if I am not mistaken is also a practicing Plaintiff's Attorney).