(CNN) During his time at one of the nation's most elite universities, there's no question that Judge Brett Kavanaugh achieved academic success. But when it comes to the frequency and severity of his drinking there, some former classmates are raising questions about how truthful Kavanaugh was in his testimony before the Senate Judiciary Committee and offering to tell FBI investigators what they know.

Former Yale classmate Chad Ludington became the latest to accuse Kavanaugh of being dishonest, saying that when he watched Kavanaugh deliver his testimony under oath to the Senate Judiciary Committee on Thursday, he "cringed" and added that he was willing to talk to the FBI.

"Brett was a frequent drinker, and a heavy drinker," Ludington said in a statement Sunday. "When Brett got drunk, he was often belligerent and aggressive. On one of the last occasions I purposely socialized with Brett, I witnessed him respond to a semi-hostile remark, not by defusing the situation, but by throwing his beer in a man's face and starting a fight that ended with one of our mutual friends in jail."

On Monday, Ludington read the statement outside his home in North Carolina and then added that "There were certainly many times when [Kavanaugh] could not remember what was going on."

Ludington told reporters he's been in touch with the FBI on Monday, and had filled out "a form," but would not elaborate.

During college, Kavanaugh was a junior varsity basketball player, a member of a secret senior society Truth and Courage and a member of one of Yale's fraternities -- Delta Kappa Epsilon -- known on campus for its occasional antics and drinking culture. But Kavanaugh has maintained that while he enjoyed beer, he wasn't drinking to the point of blacking out. And he has repeatedly denied that he ever sexually assaulted anyone.

Kavanaugh's drinking and the question of how excessive it was became a key line of questioning for Democrats on the Judiciary Committee last week and a possible credibility test for senators voting on his confirmation. Both Christine Blasey Ford, who accused Kavanaugh of shoving her into a bedroom, pinning her down and attempting to take her clothes off at a party in the 1980s, and Deborah Ramirez, who alleged Kavanaugh of exposing himself to her at a dorm room party freshman year of college, say Kavanaugh of was under the influence of alcohol when the alleged incidents occurred.

Kavanaugh said during the hearing that he drank beer not only in college, but also in high school, where, he noted, the drinking age was 18. But he disputed that he ever became blackout drunk, unable to remember events that occurred while he was under the influence of alcohol.

"I drank beer with my friends. Almost everyone did. Sometimes I had too many beers. Sometimes others did. I liked beer. I still like beer," Kavanaugh said. "I did not drink beer to the point of blacking out, and I never sexually assaulted anyone. There is a bright line between drinking beer, which I gladly do and which I fully embrace, and sexually assaulting someone, which is a violent crime."

Classmates who remember Kavanaugh being a heavy drinker have also come forward just as the FBI has reopened its background investigation into the judge.

"I've known Brett since the beginning of freshman year. He was always one of the beer drinking boys and I drank beer with him. I like beer. There's no problem with drinking beer in college. The problem is lying about it," Liz Swisher, a former classmate of Kavanaugh's, said on CNN's "Cuomo Prime Time" last week.

"He drank heavily. He was a partier. He liked to do beer bongs. He played drinking games. He was a sloppy drunk. He was more interested in impressing the boys than he was in impressing the girls. I never saw him be sexually aggressive but he definitely was sloppy drunk," Swisher added.

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Lynne Brookes, former roommate to Ramirez, also spoke on Cuomo's show to dispute Kavanaugh's testimony saying that a number of her Yale classmates were "extremely disappointed" in Kavanaugh's characterization of himself.

"There is no doubt in my mind that while at Yale, he was a big partier, often drank to excess. And there had to be a number of nights where he does not remember," Brookes said.

"In fact, I was witness to the night that he got tapped into that fraternity, and he was stumbling drunk in a ridiculous costume saying really dumb things. And I can almost guarantee that there's no way that he remembers that night," Brookes added.

Whether the FBI will examine Kavanaugh's alcohol consumption as part of its supplemental investigation isn't clear. James Roche, one of Brett Kavanaugh's freshman year roommates at Yale, tweeted Monday that the FBI had never contacted him "for any of their background checks. "

"I assume college behavior was not a topic of interest. They did not find Debbie's story because they were not looking for it." Roche said referring to allegations from Ramirez.

Roche previously said in a statement that Kavanaugh "became aggressive and belligerent when he was very drunk."

According to a 1985 police report obtained by CNN , Kavanaugh was accused of starting an altercation at a bar while he was an undergraduate student at Yale.

A man named Dom Cozzolino said Kavanaugh had thrown ice on him and Kavanaugh's friend Chris Dudley had thrown a glass that hit him in the ear, according to the report from the New Haven, Connecticut, police department. Cozzolino "was bleeding from the right ear," according to the report, and was later treated at a local hospital.

Ludington told CNN's Chris Cuomo on "Cuomo Prime Time" on Monday that he was with Kavanaugh and Dudley that night. Kavanaugh responded to an aggressive statement from Cozzolino by throwing ice at him, Ludington said, sparking a fight. They had all been drinking at a bar after attending a UB40 concert.

Dudley denied the allegations, according to the police report, "and Mr. Kavanaugh didn't (want) to say if he threw the ice or not. "

The police report does not indicate whether anyone was arrested, and New Haven's police chief, Anthony Campbell, told CNN there are no other records he is aware of involving Kavanaugh. The New York Times first reported the incident.

Following the release of the Times report, White House press secretary Sarah Sanders called the story "ridiculous."

"Democrats desperately attack Judge Kavanaugh for throwing ice during college. What motivated New York Times reporter to write this ridiculous story? Throwing ice 33 years ago, or her opinion of Judge Kavanaugh in July?" Sanders said on Twitter, pointing to a tweet from New York Times reporter Emily Bazelon in July disassociating herself from praise of Kavanaugh.

President Donald Trump has stood by Kavanaugh, but seemed to veer off script Monday when he said that he was "surprised at how vocal" Kavanaugh was about discussing his beer drinking.

"He's had a little bit of difficulty," Trump said. "He talked about things that happened when he drank."

Former college classmates have stood by Kavanaugh saying that while they may have drank with Kavanaugh, they never saw him in a state where he wasn't aware of his actions.

Dwayne Oxley, who lived on the same floor as Kavanaugh for several years in Ezra Stiles College said he "never saw [Kavanaugh] in a state where he wasn't in control."

Chris Dudley, a close friend of Kavanaugh's who was in the same fraternity and has stayed in touch with him, said Kavanaugh was never aggressive or belligerent when he drank.

"He wasn't that type of person," Dudley told CNN.

On Monday, the White House released joint statements from Dudley and a former Yale suitemate Dan Murphy refuting any claims that Kavanaugh drank to the point of blacking out.

"I never saw Brett black out or not be able to remember the prior evening's events, nor did I ever see Brett act aggressive, hostile, or in a sexually aggressive manner to women" Murphy said in a statement.

At least one former fraternity brother says reports of Delta Kappa Epsilon being a magnet for men looking to drink excessively are blown out of proportion.

"The notion that [Kavanaugh] was part of a party fraternity is not the case," said Christopher Munnelly who was a few years behind Kavanaugh and graduated in 1990.

Munnelly told CNN that at the time, Delta Kappa Epsilon did not even have a fraternity house.

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"You can't have animal house without a house," Munnelly said. "The notion that [Kavanaugh] was part of a party fraternity is not the case."

The issue of Kavanaugh's alcohol consumption has become a credibility test for some lawmakers, a question of not only who Kavanaugh was as a young man, but who he is today as he answered questions for hours before the committee last week.

During a notably tense exchange Thursday, Minnesota Democratic Sen. Amy Klobuchar asked Kavanaugh if he had ever woken up and not been able to remember what happened -- or part of what happened -- the night before after drinking too much. Kavanaugh turned thre question of Klobuchar.

"You're asking about, you know blackout. I don't know. Have you?" he asked, later apologizing for turning the question back on the senator.

"I was really stunned by how he acted at that hearing," Klobuchar told CNN's State of the Union Sunday. "One idea here is that he simply was drinking more than he was saying over this time period, and that he didn't remember what happened so I was just simply trying to get at that."