The authority of an investigation of the California Supreme Court was challenged today when Chief Justice Rose Elizabeth Bird refused to answer a half dozen questions by the State Commission of Judicial Performance.

The refusals, on questions involving supposed court leaks to the press, could force a confrontation between Bird and the commission. Though the commission has no power to cite her for contempt, special counsil Seth M. Hufstedler said that it could go to court to obtain an order compelling the chief justice to answer.

Hufstedler said that if Bird then continued her refusals to answer, she could be fined or jailed, as courts have done with newspaper reporters who have declined to identify their sources.

It is not clear when a showdown will come, if at all. Up to now, the commission, half of whose members are oppointed by the court it is investigating, has tried to avoid confrontations in its probe into purported unethical conduct by the court. However, Hufstedler said that by the end of the week he would ask the commission to reach a decision as to whether it will seek the withheld information.

Neither Hufstedler nor Commission Chairman Bertram D. Janes, a veteran California appellate justice, would predict what the commission would do.

"It may be a tempest in a teapot or it may be vitally important," Hufstedler said.

The commsission is in its third week of hearings to determine if justices delayed controversial court opinions after last November's election, when Bird and three other justices faced voter confirmination and if justices or their aides leaked information about the opinions to the press in violation of a judicial canon.

Near the end of Bird's testimony today, Hufstedler asked her whether her staff had delivered documents to her containing information about the leaks that had not been turned over to the commission.

"I have no comment," Bird replied.

Addressing himself to Janes, Hufstedler replied: "I'm not looking for a comment. I'm looking for an answer to my question, Mr. Chairman."

Janes directed the chief justice to answer and she refused on the advice on her attorney, Harry Dilizonna, who said he has been directing an "independent investigation" into the source of the leaks.

Dilizonna apparently based his advice on the commission's lack of authority to subpoena anyone beyond a 150-mile radius of San Francisco. A witness beyond that area could be required to give a deposition but could not be compelled to come to the commission and testify. If such a person were publicly indentified, he or she would have the opportunity to avoid a subpoena.

Whether the information the commission wants is important of itself, Bird's refusal to give it raise fundamental questions akin to those confronting Congress before the U.S. Supreme Court ordered the White House to surrender the Watergate tape recordings.

At this point, the commission appears to be fighting a guerrilla war not with an executive branch but with the state's court over its authority. Privately, there is some concern among lawyers here that the challenges could impair the ability of the commission to gather information, court whose turmoil and hostilities have been widely publicized.

Justice Frank Newman, who has yet to testify, declined to furnish confidential memoranda to the commission. There are reports that Justice Stanley Mosk, the last scheduled witness, will refuse to testify at a public proceeding.

And Justice William P. Clark, who began testimony today under subpoena, said he would answer all questions put to him but questioned the constitutionality of a public investigation.