Washington (CNN) In the two weeks since Chief Justice John Roberts referred a series of misconduct complaints against Justice Brett Kavanaugh to a Denver-based appeals court, many experts on judicial discipline have predicted the complaints will never be resolved.

The 15 specific claims, arising from Kavanaugh's Senate testimony last month, including after he was accused of sexual assault, were funneled into a system of self-policing that has been under scrutiny for nearly a year. Members of Congress, women's rights advocates and other critics have questioned whether the system, which fields hundreds of claims annually and is largely hidden from public view, holds judges accountable.

The complaints against Justice Kavanaugh are unlikely to go anywhere for their own distinct reasons.

Supreme Court justices have long been exempted from the US judiciary's disciplinary rules, so it is doubtful the Denver-based 10th Circuit judicial council under Chief Judge Timothy Tymkovich would ultimately find jurisdiction to investigate Kavanaugh.

There may be another reason to reject any complaints related to Kavanaugh's statements denying Christine Blasey Ford's claim that he sexually assaulted her when they were both teenagers. In an unrelated case last year, the 10th Circuit council suggested judges should not review allegations arising from testimony during the Senate confirmation process, based on the constitutional separation of powers.

In his correspondence directed to Tymkovich, Roberts did not say why he was referring the matter to that circuit beyond including letters from the US Court of Appeals for the District of Columbia Circuit, where Kavanaugh served for 12 years, noting that "local disposition may weaken public confidence in the process."

Tymkovich, who since September 2016 has been on President Donald Trump's list of potential candidates for the Supreme Court, was appointed to a life-tenured appeals court seat by President George W. Bush in 2003, when Kavanaugh was in the White House counsel's office and screening judicial candidates.

In Kavanaugh emails made public during his recent confirmation process, it is clear Kavanaugh followed Tymkovich's prospects from his May 2001 nomination until his April 2003 Senate approval.

A spokesman for Tymkovich said that the judge would have no comment on the Kavanaugh referral or any potential conflict of interest. The Guardian newspaper first reported on Kavanaugh's involvement in Tymkovich's appointment on Monday.

How much Kavanaugh may have influenced the selection and confirmation of Tymkovich, a former Colorado state solicitor general, is not clear from the Kavanaugh correspondence released.

A separate review of Kavanaugh's Senate testimony has already dissolved. The American Bar Association had said it was reevaluating the "well qualified" rating it had previously given Kavanaugh because of the sexual assault allegations and his response during September 27 testimony. But the group dropped that review after Kavanaugh's October 6 Senate confirmation.

To many lawyers, professors and others who watched Ford and Kavanaugh before the Senate Judiciary Committee, the judge's reaction was nearly as startling as Ford's claims. In his televised testimony, Kavanaugh declared that Ford's sexual assault allegations arose from "a calculated and orchestrated political hit, fueled with apparent pent-up anger about President Trump and the 2016 election ... revenge on behalf of the Clintons and millions of dollars in money from outside left-wing opposition groups."

The former Bush aide who previously served with independent counsel Ken Starr's investigation of President Bill Clinton also asserted, "As we all know, in the United States political system of the early 2000s, what goes around comes around."

After a flood of criticism, much of which questioned whether he had the temperament to be a judge, Kavanaugh wrote an October 4 essay for the Wall Street Journal, acknowledging, "I was very emotional last Thursday, more so than I have ever been. I might have been too emotional at times. I know that my tone was sharp, and I said a few things I should not have said."

The Kavanaugh complaints have not been publicly detailed beyond the characterization that they are related to statements he has made, not conduct on while on the bench.

No information on their resolution would be available until an order on the matter is made public on the 10th Circuit website, according to Circuit Executive David Tighe. Chief Judge Tymkovich did not respond to a CNN request for information about the Kavanaugh matter.

A controversial system

The US judiciary's process for handling complaints against sitting judges burst into the headlines late last year after several women publicly accused former 9th US Circuit Court of Appeals Chief Judge Alex Kozinski of sexual harassment.

Under federal rules, complaints against judges go first to the appropriate chief judge in the country's 13 circuit courts. The overwhelming number come from disgruntled litigants, and it appears that courthouse employees or others with arguably valid complaints against judges do not use the system.

After the Kozinski complaints, the Senate Judiciary Committee questioned James Duff, director of the administrative office of the US Courts, about potential problems of sexual harassment in the nation's courthouses. (Kozinski denied any wrongdoing and left the bench soon after the Washington Post first detailed allegations of sexual harassment from former law clerks and other staffers.)

Duff said such accusations are rare. "In 2018, a judge alleged inappropriate conduct by another judge toward an employee," Duff wrote in a July 31 letter to the Senate Judiciary Committee, adding that the employee did not file a formal complaint and that "the matter was resolved to the satisfaction of the employee." Duff said the judge was "no longer on the bench." He also alerted the committee to incidents in 2013 "involving sexual harassment by another employee," and in 2016, alleging "inappropriate conduct by a judge."

Both were resolved with "nominal monetary relief" of less than $25,000 combined, Duff said. David Sellers, spokesman for the administrative office, said no other details on those incidents were available.

Last December after the Kozinski reports, Roberts in set up a special group to examine the judiciary's misconduct procedures and protections for employees. A hearing on recommendations has been scheduled for October. 30.

Roberts also transferred complaints about Kozinski from the California-based 9th Circuit, where Kozinski had served since 1985, to the New York-based 2nd Circuit council.

That judicial council in February dismissed the sexual harassment complaints against Kozinski because he had retired.

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Supreme Court justices not investigated?

What emerges from the 10th Circuit on Kavanaugh may not illuminate the situation, because nothing in the judiciary's past practices suggests the judicial council will address the merits of the filings.

That is because the 1980 federal ethics law that governs complaints does not cover Supreme Court justices.

"The 10th Circuit will almost certainly conclude that intervening events make it impossible to investigate," said University of Pittsburgh law professor Arthur Hellman, referring to Kavanaugh's elevation to the high court.

Hellman, who has studied the judicial misconduct process for decades, speculated that Tymkovich would not issue a brief, perfunctory, order.

"A lot of people care about this," Hellman said. "He's not going to want to write an opinion that says only the law ties our hands. I would think he might want to write an opinion that puts it in historical and constitutional perspective."

Hellman and others say Congress chose not to include Supreme Court justices in the 1980 Judicial Conduct and Disability Act because of their position at the helm of the Third Branch delineated in the Constitution and because it might have appeared unseemly for the justices to fall under the authority of any lower court disciplinary panel.

Russell Wheeler, a visiting fellow of governance studies at the Brookings Institution, who has similarly studied the judiciary, agreed that no investigation of the filings would likely be made. He said the current situation involving a judge-turned-justice was unprecedented.

Yet, Wheeler observed, jurisdiction has evaporated in other situations such as when a judge retired, as happened with Kozinski earlier this year and, a year earlier, when US District Court Judge Walter Smith, of Texas, retired while a complaint of sexual misconduct was pending.

When Chief Justice Roberts transferred the complaints filed at the DC Circuit, he said they covered three on September 20; three on September 26, two on September 28, one on October 3, and six on October 5.

The grievances were originally conveyed to Roberts from DC Circuit Judge Karen LeCraft Henderson. In an October 6 release about the matter, Henderson observed that "members of the general public began filing complaints" after Kavanaugh's first round of hearings before the Senate in early September. She said the filings did not involve "any conduct" as a judge, but rather "statements ... as a nominee."

Under the usual process, the DC Circuit Chief Judge Merrick Garland would have taken the leading role in deciding how to handle the Kavanaugh complaints.

Garland, without any public comment, apparently recused himself. Garland was once a Supreme Court nominee himself. The Republican-controlled Senate stalled his 2016 nomination by Democratic President Barack Obama for nearly a year, and then picked up on filling the open ninth seat after Trump became president in January 2017. That went to Justice Neil Gorsuch, now joined on the high court by Kavanaugh.