I have long complained that activist Republican ideologues, Antonin Scalia and Clarence Thomas had a conflict of interest in the Citizens United and other nefarious decisions. I covered this last March in Teabuggery Reaches the Extreme Court and last December in When Scalia Goose Steps with the Tea Party. I’m pleased to report that Common Cause has filed a petition claiming exactly that.

When the conservative financier Charles Koch sent out invitations for a political retreat in Palm Springs later this month, he highlighted past appearances at the gathering of “notable leaders” like Justices Antonin Scalia and Clarence Thomas of the Supreme Court.

A leading liberal group is now trying to use that connection to argue that Mr. Scalia and Mr. Thomas should disqualify themselves from hearing campaign finance cases because they may be biased toward Mr. Koch, a billionaire who has been a major player in financing conservative causes.

The group, Common Cause, filed a petition with the Justice Department on Wednesday asking it to investigate potential conflicts by Justices Scalia and Thomas and move for their disqualification from the landmark Citizens United case, in which the court last year lifted a ban on corporate spending on political campaigns. Common Cause also cited the role of Mr. Thomas’s wife, Virginia Thomas, in forming a conservative political group opposed to the Obama administration as grounds for his disqualification.

The petition is a new tack for opponents of the court’s decision in the Citizens United case. Common Cause, by its own acknowledgment, faces a difficult task in getting the justices’ to remove themselves from the case and seeking to have the Citizens United decision itself vacated.

“We’re treading in new territory here for us,” said Arn H. Pearson, Common Cause’s vice president for programs. “But a situation like this raises fundamental questions about public confidence in the Supreme Court.”

Officials at Koch Industries, which Mr. Koch leads, did not respond to e-mails and a phone call Wednesday seeking comment on the petition. A spokeswoman at the Supreme Court declined comment.

Supreme Court justices have wide latitude in deciding whether to recuse themselves from hearing cases. In one of the more well-known examples in recent years, Justice Scalia refused to remove himself from hearing a challenge to Vice President Dick Cheney’s energy task force after he had gone duck hunting with Mr. Cheney in 2004.

“It’s a steep uphill climb for Common Cause, but not an insurmountable one,” said Steven Gillers, who teaches legal ethics at New York University. At the very least, he said, the group’s petition could force a “public airing” of questions surrounding the two justices’ past appearances at the Koch retreat and their connections to the group… [emphasis added]