The actor filed a motion asking the court to remove Andrea Reeb, as she also serves in the state House of Representatives.
The accuser first filed the lawsuit in December but hadn't named the rock star.
Girardi on Wednesday was indicted by federal grand juries in Chicago and Los Angeles.
The 'Low' rapper took a sip out of the energy drink after the jury sided with him.
The reality star is asking the presiding judge in her case for a three-year prison sentence.
James Howard Jackson, one of the men responsible for the crimes, pleaded no contest to one count of attempted murder.
The decision comes nearly two years after he was ordered to stand trial.
The filmmaker was found liable for raping a woman in Manhattan in 2013.
The TV producer and writer was remanded into custody after previously being out on $5 million bail.
The actor filed a petition on Tuesday arguing that the judge in his case is allegedly biased against him.
Attorneys for the plaintiffs began delivering their closing arguments Tuesday in Los Angeles federal court.
The pair headed into court on Monday amid their ongoing lawsuit against Los Angeles County.
The actress' lawyers are asking a judge to toss out the $10.35 million verdict against her, citing lack of evidence and juror problem.
The cosmetics mogul is accused of stealing the skin care line's logo from the Brooklyn-based company Beauty Concepts.
