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.