12/11 4:02 PM PT -- Yale President, Peter Salovey, has released a statement on the incident ... claiming it's still unknown if the perpetrator was an actual student at Yale, and correcting information floating around stating the incident happened on campus.

Salovey's statement reads, "Yale condemns in the strongest possible terms the desecration of a menorah on the New Haven Green during the religious holiday of Chanukah. The placement of a Palestinian flag on the menorah conveys a deeply antisemitic message to Jewish residents of New Haven, including members of the Yale community."

He continues, "Yale’s regulations reach conduct occurring on or off campus that imperils the integrity and values of the University community, and if such conduct is committed by a member of the Yale community, we take action. Yale has asked the New Haven police to investigate this incident and Yale may conduct its own investigation. Desecration of property such as a religious object is a crime under Connecticut law."

Salovey says the school does not yet have any info on whether or not the suspect is a member of the Yale community.

A pro-Palestinian student at Yale tried to co-opt the symbol of the current Jewish holiday by planting a Palestinian flag on a menorah.

The student climbed the oversized menorah, the symbol of Hanukkah, as others screamed, "Get the f**k down!," and "It looks bad for us" ... as seen in viral video posted by attorney Jake Dressler.

One student is seen climbing the menorah to 86 the flag. The flag has now been removed.

It's the latest skirmish on college campuses around the country -- especially elite colleges and universities. As you know, the President of the University of Pennsylvania resigned Saturday after a torrent of criticism over her testimony in Congress Monday, where she would not squarely say calling for the genocide of Jews was bullying or harassment.