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The defense attorneys for Joshua Komisarjevsky filed a motion for Blue to be disqualified from hearing the case, claiming that he showed "partiality, lack of objectivity and unsuitable temperament" during the trial for the other defendant, Steven Hayes.
Hayes was convicted for his role in the slayings of Jennifer and Hayley, 17, and Michaela, 11, in their Cheshire home and sentenced to death.
Judge Brian Fischer presided over the hearing on Tuesday.
After hearing from the defense and prosecutors, Fischer said Blue didn't show bias or give rise to question his impartiality and said Blue could preside over the trial.
Defense attorneys also brought up reporters tweeting from the courtroom and complained about the judge bringing chocolate chip cookies and giving them out at court.
They said they want to pursue another motion to have Blue removed.
After a recess, Blue will hear additional motions.