Cops roughed up a man sleeping in a Brooklyn synagogue in a confrontation that was caught on surveillance video — and the police officers are now drawing criticism from city officials who say they overreacted.

The Oct. 8 beat-down happened at the Alternative Learning Institute for Young Adults, a Crown Heights synagogue and outreach center for troubled youth. Cops apparently believed that the man — identified as 21-year-old Ehud Halevy –was homeless and trespassing.

Volunteer security guard Ziamy Trappler, 24, had called cops after seeing the shirtless and pants-less Halevy sleeping on a couch by a pool table, center officials said.

But Rabbi Moshe Feiglin, who runs the youth center, said the beaten man was not trespassing and had been staying there for a month and that the call to cops was all just a misunderstanding.

Some city politicians called a press conference today to decry the actions of the two cops, who are from the 71st Precinct.

“When we watched the video and saw some of New York’s finest behaving in a not very fine way, brutalizing an individual for absolutely no reason, it was just something horrible,” said Brooklyn Assemblyman Dov Hikind.

Joining him were Public Advocate Bill de Blasio, Comptroller John Liu, city Councilwoman Letisha James and several Jewish community leaders.

“This person had permission to be there,” Hikind said. “There was no issue. Regardless, the behavior of the police department, of two individuals, is beyond comprehension, a very sad moment for me personally.”

NYPD officials had no immediate comment.

Mayor Bloomberg said he hadn’t seen the video and declined to discuss it.

Halevy was arrested for arrested for assaulting a police officer, resisting arrest and trespassing.

Hikind called for cops involved in the beating to be suspended.

“This behavior in unconscionable, and if not for the video recorder to record what happened, we might actually believe that Ehud attacked the police officers. And he never did,” the lawmaker said.

“These officers must be suspended, if they have not been suspended. They cannot be out there protecting the public. We need to be protected from them.”

Cops said Haleavy was in a section of the center that’s meant for women.

“Police responded to a call of a dispute inside of a synagogue’s outreach center in Brooklyn, where a man refused to vacate the women’s portion of the center,” said NYPD spokesman Paul Browne.

“The officers used force to affect the arrest”

Haleavy was charged with assault, trespass, resisting arrest, harassment, and unlawful possession of marijuana. Haleavy’s defense lawyer could not be immediately reached for comment.

NYPD Internal Affairs Bureau investigators are reviewing the arrest, Browne said one of the officers involved, a 49-year-old man, “has been placed on modified assignment while the incident is under investigation.”

Brooklyn prosecutors are also taking a close look at the incident.

“The Brooklyn DA is looking at the tape and investigating the circumstances of the arrest,” a law enforcement source said,

Additional reporting by Jamie Schram, David Seifman and David K. Li