WASHINGTON — The chairman of the Senate Judiciary Committee on Thursday referred a woman who accused Justice Brett M. Kavanaugh of sexual misconduct for criminal investigation, questioning whether she and her high-profile lawyer, Michael Avenatti, knowingly provided the committee with false information.In a letter to the attorney general and the F.B.I. director, the chairman, Senator Charles E. Grassley, Republican of Iowa, detailed a series of apparent contradictions between sworn claims submitted to his committee and subsequent statements to the news media by the woman, Julie Swetnick, and Mr. Avenatti, who could also be investigated. Mr. Grassley also said that committee investigators had been able to find no information substantiating the claims and instead unearthed “substantial information calling into question her credibility.”“For the law to work, we can’t just brush aside potential violations,” Mr. Grassley said in a statement accompanying the letter. “I don’t take lightly making a referral of this nature, but ignoring this behavior will just invite more of it in the future.”Mr. Avenatti, who is better known for representing Stephanie Clifford, the pornographic film actress also known by her stage name, Stormy Daniels, who has taken on President Trump, responded with characteristic bravado in a pair of tweets. He called Mr. Grassley’s interest in investigating “ironic” but said he welcomed the inquiry as a means to “get to the bottom of Judge Kavanaugh’s lies and conduct.” He did not address Mr. Grassley’s statement about apparent inconsistencies.The Justice Department is not obligated to take up the matter, and the department and the F.B.I. declined to comment. But in making a high-profile referral several weeks after Justice Kavanagh was confirmed, Mr. Grassley was all but sure to reignite the partisan sniping that engulfed the confirmation fight and has seemingly boosted Republicans’ bid to retain control of the House and Senate in next month’s midterm elections.Mr. Avenatti submitted a sworn statement by Ms. Swetnick to the Judiciary Committee on Sept. 26, as lawmakers were in the throes of untangling the accusations of two other women, Christine Blasey Ford and Deborah Ramirez, who said a younger Justice Kavanaugh had sexually assaulted them in high school and college, respectively.Ms. Swetnick’s claims were more graphic. She said that she “became aware” of the future Supreme Court justice spiking punch at parties in the early 1980s in an attempt to intoxicate women and take advantage of them. She also said she remembered seeing him among a group of “numerous boys” lined up outside a bedroom, “waiting for their ‘turn’ with a girl inside the room.”Justice Kavanaugh denied the charges of all three women.In building a case to the authorities, Mr. Grassley’s letter cites an Oct. 1 interview with NBC News in which Ms. Swetnick appeared to alter some of those claims and contradict a timeline laid out in her declaration to the committee, as well as interviews with Mr. Avenatti.The letter says investigators working for Mr. Grassley contacted 10 people who knew Ms. Swetnick, 55. None could corroborate her claims, but raised questions about her credibility, including the appearance that “Ms. Swetnick has a history of making false legal claims and false accusations of sexual misconduct.” The letter also lays out “substantial credibility issues” relating to Mr. Avenatti.The arrival of Ms. Swetnick’s claims only a day before a high-stakes hearing with Dr. Blasey and Justice Kavanaugh further inflamed what was already a tense debate among Republicans and Democrats over what to do about the 11th-hour accusations.Democrats called for the hearing and nomination to be delayed so the F.B.I. could investigate the claims of all three women. Republicans vowed to do it themselves, pushed ahead and within a day used Ms. Swetnick’s claims to accuse Democrats of conspiring in a smear campaign to derail the nomination.When, a little more than a week later, they confirmed Justice Kavanaugh on a nearly party-line vote, Republicans credited the “over the top” claims by Ms. Swetnick and Mr. Avenatti with uniting the party around the embattled nominee.The accusations and the fight that ensued appear to have contributed to increased enthusiasm among the conservative voters that Republicans need to stave off losses at the polls on Nov. 6. Mr. Trump and the party’s candidates have painted the episode as a preview of Democratic “mob rule” that would govern the Capitol if the Democrats win power.The referral was not Mr. Grassley’s first related to Justice Kavanaugh’s accusers. Late last month, he referred to investigators the case of a Rhode Island man who claimed to one of the Judiciary Committee’s members that the nominee had sexually assaulted a woman he knew in 1985 on a boat in Newport, R.I. After the committee released an unequivocal denial by Justice Kavanaugh, the man, who was never publicly identified, recanted his story.