In a two-page letter dated 14 October and obtained by the BBC, Doe told the faculty senate that after she reported the alleged rape, she received "a second-hand account" of Kotlikoff's reaction and that his "initial response" was "along the lines of, 'Why did she wait so long to report it?'"
Doe reported the alleged assault to campus police on 8 November, about three weeks after the fraternity party.
She noted that Kotlikoff had a conversation with the then-president of her sorority and that other staff members were present, at least one of whom "appeared distressed" by the college president's question.
Doe said in her letter: "It diminished my confidence in the administration's ability to approach my experience with the understanding, sensitivity, and fairness I had hoped for and expected from what had been my dream school."
She said she wrote the letter so that faculty "can make an informed choice" ahead of their 28 October vote on whether to express no confidence in Kotlikoff's leadership.
The university confirmed receipt of the letter from Doe's lawyer.
But in a statement to the BBC, a Cornell spokesperson said: "The second-hand account of the question asked by President Kotlikoff in a January 2025 meeting in the letter is incorrect, based on a documented first-hand account."
The spokesperson said Kotlikoff's question about the delay in reporting the alleged rape "was directed at bystanders who did not use Cornell's anonymous tip line, despite ongoing social media activity about the incident in October 2024".
"He was not questioning Jane Doe's reporting," the spokesperson said.
Kotlikoff, who has led the Ithaca-based institution for 26 years, was grilled by the faculty senate last Wednesday.
Staff said they were "deeply disturbed" by his handling of the case and accused him of lacking an "emotional response", according to recordings obtained by the BBC.
Kotlikoff highlighted changes the university had introduced as a result of Doe's allegations, including banning fraternity parties.
"We are all extraordinarily upset by the events at Cornell in October of 2024," he said.
The faculty senate, a governing body composed of professors and other academic staff at Cornell, scheduled their no-confidence vote for 28 October.
In recordings of the meeting, faculty said sexual misconduct on campus was a systemic problem that demanded "systemic attention".
Paul Ortiz, a labour history professor who sponsored the no-confidence resolution, said students had told faculty they "feel unsafe walking to the library after dark".
He accused Cornell of treating rape "as more of a 'PR problem' than a heinous crime".
With additional reporting by Pratiksha Ghildial.