At a history class, a professor mockingly tells a female Jewish student she cannot possibly have ancestral ties to Israel because her eyes are green.

During a lecture, a professor of Arab politics refuses to answer a question from an Israeli student and military veteran but instead asks the student, "How many Palestinians have you killed?"

At a student meeting on the topic of divestment from Israel, a Jewish student is singled out as responsible for death of Palestinian Arabs.

Those scenes are described by current and former students interviewed for an underground documentary that is causing a frisson of concern to ripple through the Morningside Heights campus of Columbia University, where the incidents took place.

The film, about anti-Israel sentiment at the school, has not yet been released to the public, but it has been screened for a number of top officials of Columbia, and talk of its impact is spreading rapidly on a campus where some students have complained of anti-Israel bias among faculty members.

"The movie is shocking," one Columbia senior, Ariel Beery, said.

"It is shocking to see blatant use of racial stereotypes by professors and intimidation tactics by professors in order to push a distinct ideological line on the curriculum," Mr. Beery, who was interviewed for the film, said.

The film is the creation of the David Project, a 2-year-old group based in Boston that advocates for Israel and is led by the founder of the American Anti-Slavery Group, Charles Jacobs. The David Project, which is refusing to make the film public, has screened it for Barnard College's president, Judith Shapiro, and Columbia's provost, Alan Brinkley, according to sources...