According to the document, which has been obtained by ABC News, at the time of the incident, Crews was represented by WME. After he informed his agent about what he says happened, "WME took no action at that time against Venit ... likely because Venit is a significant moneymaker for WME."
Crews has since fired his WME agent.
"It is now time to hold Venit accountable for his sexual predatory behavior and to hold WME accountable for its conduct in condoning, ratifying, and encouraging Venit’s sexual predatory behavior," the lawsuit reads. "Indeed, a message needs to be sent to those in power who abuse those over whom they exert influence and control that abusive and sexual predatory behavior will not be tolerated."
A request for comment from Venit or WME was not immediately returned to ABC News.
This lawsuit, which demands a jury trial and seeks unspecified damages, comes less than a month after Crews filed a police report on Nov. 8, a source inside the Los Angeles Police Department confirmed to ABC News at the time.
"I have never felt more emasculated, more objectified. I was horrified," Crews said. "It's so bizarre. I wake up every morning wondering, 'Did this really happen?'"
"People need to be held accountable," he added. "This is the deal about Hollywood. It is an abuse of power. This guy, again, he's one of the most powerful man in Hollywood, and he looked at me at the end as if, 'Who is going to believe you?'"
While Venit did not respond to ABC News requests for comment at the time of the interview, William Morris Endeavor stated, "Adam Venit was suspended following the internal investigation into the matter."
Weinstein has been accused by dozens of women of sexual misconduct, but he has denied all allegations of non-consensual sex.