Robert and Arlene Holmes say their son is mentally ill and should be placed in an institution for the rest of his life.
Aurora Theater Shooting
James Holmes pleaded not guilty by reason of insanity to charges of killing 12 people and injuring 70 in the 2012 attack at a Denver-area theater.
Defense attorneys said Judge Carlos A. Samour Jr. takes a hostile and demeaning tone toward them in his rulings.
The report concluded that the "outcome could not have been better in terms of lives saved and a rapid arrest."
The lawsuit was announced Tuesday by attorneys for the parents a victim and the Brady Center to Prevent Gun Violence.
The justices did not comment on Tuesday, leaving in place a decision by New York's top appellate court that shielded Fox News reporter Jana Winter from being called to testify in a Colorado court.
Petra Hogan talks about her music and her recovery after sustaining a shotgun pellet in the brain during the mass shooting at a Aurora movie theater in 2012.
Lawyers for accused Aurora theater shooter James Holmes are appealing a judge's decision to conduct a second psychiatric evaluation of their client.