Park`s lawyers said one of the court`s eight judges, Kang Il-won, had consistently shown bias in his questioning of witnesses and had admitted questionable evidence.
"If this judge participates in this case ... it could harm the fairness of the trial, which is the basis of our request to remove him," a lawyer for Park, Cho Won-ryong, told the hearing.
"According to our analysis, Judge Kang mostly asks questions to the defense`s witnesses," Kim Pyung-woo, another lawyer for Park said. "And his questions for the defense witnesses always start off with criticism."
Park has not appeared before the court. It can not order her to appear - she retains presidential immunity while in office - and her lawyers have said she has not decided whether to attend.
The corruption scandal erupted late last year over accusations that Park colluded with a friend, Choi Soon-sil, to pressure big businesses to donate to two foundations set up to back the president’s policy initiatives.
Park, 65, was impeached by parliament in December and she has been stripped of her powers while the Constitutional Court decides whether to uphold the impeachment.
The daughter of a former military ruler, Park has denied wrongdoing, as has Choi.
If the impeachment is upheld, Park would become the first democratically elected leader to be removed from office and a new election would have to be called in 60 days to pick a new leader for a full five-year term.
The court says it would conclude oral arguments on Feb. 27. It has not said when it would deliver a verdict but according to past practice, a decision could be expected after about two weeks.
For the impeachment to stand, at least six of the eight judges must rule in its favor. The seat for the court`s ninth judge was vacated when its chief retired at the end of January.
In a case linked to the scandal, the chief of South Korea`s biggest conglomerate, Samsung Group, was arrested on Friday on suspicion of bribing Park`s friend to gain government favors.
Samsung and its chief, Jay Y. Lee, have denied wrongdoing.
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