Washington (CNN) Anita Hill called on the federal government to implement a "fair and neutral" way to investigate sexual misconduct complaints after allegations surfaced against Supreme Court nominee Brett Kavanaugh this week.

Hill, who accused Supreme Court Justice Clarence Thomas of workplace sexual harassment during his confirmation hearing back in 1991, said she has seen "firsthand what happens when such a process is weaponized against an accuser and no one should have to endure that again."

Then a law professor at the University of Oklahoma, Hill testified before the Senate Judiciary Committee that she had been sexually harassed by Thomas when she worked with him at the Education Department and Equal Employment Opportunity Commission. Thomas denied the allegations and he was confirmed to the bench.

A woman is accusing Kavanaugh of assaulting her when they were high schoolers in the early 1980s, and she relayed the claim in a letter to Democratic Sen. Dianne Feinstein of California, who received the note in July and referred it to the FBI on Wednesday.

Kavanaugh has vehemently denied the allegation, saying in a statement: "I did not do this back in high school or at any time."

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