Sen. Tom Cotton Tom Bryant CottonThe Hill's 12:30 Report: Trump stokes fears over November election outcome The Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Abortion stirs GOP tensions in Supreme Court fight MORE (R-Ark.) asserted on Sunday that Sen. Dianne Feinstein Dianne Emiel FeinsteinTrump faces tricky choice on Supreme Court pick The Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Abortion stirs GOP tensions in Supreme Court fight MORE (D-Calif.) will face an investigation over her handling of a letter from Christine Blasey Ford in which she alleged Supreme Court nominee Brett Kavanaugh sexually assaulted her decades ago.

Appearing on CBS's "Face the Nation," Cotton disputed the legitimacy of Feinstein's claim that she did not disclose Ford's letter to Senate Judiciary Committee Chairman Chuck Grassley Charles (Chuck) Ernest GrassleyGOP lawmakers distance themselves from Trump comments on transfer of power The Hill's 12:30 Report: Ginsburg lies in repose Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy MORE (R-Iowa) because Ford had asked it remain private.

"They have betrayed her. They pointed her to lawyers who lied to her and did not tell her that the committee staff was willing to go to California to interview her. Now all of that is water under the bridge," Cotton said.

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"Those lawyers are going to face a D.C. bar investigation into their misconduct," he continued. "Dianne Feinstein and her staff is going to face an investigation for why they leaked that."

WATCH: "Those lawyers are going to face a D.C. bar investigation into their misconduct. Dianne Feinstein and her staff is going to face an investigation into their misconduct," @SenTomCotton tells @FaceTheNation https://t.co/gQQdnAYUMb pic.twitter.com/zzHboxnXzD — Face The Nation (@FaceTheNation) September 30, 2018

Cotton did not elaborate on who would conduct such an investigation, but Feinstein, the ranking Democrat on the Senate Judiciary Committee, has adamantly denied that her office leaked Ford's letter.

Feinstein's office did not immediately respond to a request for comment.

Feinstein first received a letter from Ford detailing the allegations in July, but Ford had asked that it remain private.

Ford went public with her allegation earlier this month that Kavanaugh pinned her to a bed and groped her during a high school party in the 1980s after reports began to surface that Feinstein turned over a letter to the FBI that included a sexual assault allegation against Kavanaugh.

Kavanaugh has denied the allegations.

Cotton took his attacks on Feinstein a step further on Sunday, arguing that if Kavanaugh is confirmed, any negative effects it has on the willingness among women to share their stories of sexual assault should be blamed on Feinstein and Senate Minority Leader Charles Schumer Chuck SchumerPelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' 3 reasons why Biden is misreading the politics of court packing Cruz blocks amended resolution honoring Ginsburg over language about her dying wish MORE (D-N.Y.).

"Any impact that this entire episode has had on women's willingness to come forward and report sexual assault, which I encourage them all to do immediately after it happens, is caused by the Democrats, is caused by Dianne Feinstein and Chuck Schumer Chuck SchumerPelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' 3 reasons why Biden is misreading the politics of court packing Cruz blocks amended resolution honoring Ginsburg over language about her dying wish MORE not respecting her requests for confidentiality," Cotton said.

Following Ford's allegation, Republicans have focused much of their criticism on Feinstein for not sharing the claim with them or with Kavanaugh earlier in the confirmation process.

At a rally Saturday night, President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE stoked speculation that Feinstein or her staff may have leaked the letter, basing his claims on her body language.