WASHINGTON (CNN) -- Two leading Democratic senators asked Chief Justice William Rehnquist on Thursday about the propriety of a hunting trip Supreme Court Justice Antonin Scalia took with Vice President Dick Cheney while Cheney has a case pending before the high court.

In a letter to Rehnquist, Sens. Patrick Leahy of Vermont and Joe Lieberman of Connecticut asked the chief justice to tell them what "canons, procedures and rules" are in place to determine when justices should recuse themselves from cases.

They also asked Rehnquist what guidance justices have been given about accepting trips, and whether the full court has any way to disqualify a member from hearing a case if a justice refuses to recuse himself.

"When a sitting judge, poised to hear a case involving a particular litigant, goes on a vacation with that litigant, reasonable people will question whether that judge can be a fair and impartial adjudicator of that man's case or his opponent's claims," the senators wrote.

"The integrity of our courts and the confidence of the American people depend on judges acting without fear or favor."

Leahy is the ranking Democrat on the Senate Judiciary Committee. Lieberman is the ranking Democrat on the Senate Governmental Affairs Committee and a 2004 presidential candidate.

In December, the Supreme Court agreed to hear Cheney's appeal of a lower court ruling ordering him to disclose details of meetings between his energy policy task force and contacts in the energy industry.

The vice president's lawyers contend that information is protected by executive privilege.

The two groups that brought the suit, Judicial Watch and the Sierra Club, insist the records should be made public so they can determine whether lobbyists for the energy industry helped craft the administration's energy policy.

Earlier this month, Cheney invited Scalia, an old friend, to accompany him on a hunting trip in Louisiana.

The two also dined together along with Defense Secretary Donald Rumsfeld at a restaurant on Maryland's Eastern Shore in November.

In a letter to the Los Angeles Times, which first disclosed details of the trip, Scalia defended his actions, saying they did not threaten his impartiality.

He said social contacts between high-level administration officials and judges "have never been thought improper" in situations where a judge is considering a case involving actions an official took in his "official capacity," rather than his "personal capacity."

Cheney is not personally liable in the task force case and would not face financial damages if he loses.

The groups involved in the lawsuit question whether the trip was proper given Cheney's business before the court -- questions echoed by Lieberman and Leahy in their letter to Rehnquist.

"While judges should not be isolated from the society in which they live, they must take special care that their extra-judicial activities do not create a conflict with their judicial duties," they wrote.

"Setting aside any evidence of actual bias, the ethical rules recognize that the perpetuation of an appearance of partiality is a threat to public confidence in our federal courts."

Members of Congress who have questions about whether actions they are about to take might violate ethics rules can ask for advisory opinions in advance.

The senators asked Rehnquist to tell them whether the Supreme Court has a similar mechanism, and whether Scalia used it before accepting the trip with Cheney.

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