He claims Depp - starring as retired LAPD detective Russell Poole, who worked on both 1990s rap star murders - requested an extension of the permit so that he could direct two of his friends in an extended version of the scene the crew was filming that day.
Brooks alleges that in April 2017, when the film was shooting under the title "Labyrinth" in and around the Barclay Hotel in downtown LA, he informed the director Brad Furman that an upcoming take featuring Depp would have to be the last outdoor shot of the night because of legal permits.
TMZ claimed Brooks went to get a police officer for protection before approaching the star, who reportedly screamed at him: "Who the f*** are you?" When Brooks didn't react to the punches, Depp supposedly said, "I will give you $100,000 to punch me in the face right now".
Depp is also now facing a lawsuit from two former bodyguards, Eugene Arreola and Miguel Sanchez, who allege that, in their assignment protecting Depp between 2016 and 2018, they "found themselves in situations that required more than what a bodyguard would be expected to do".
A source told Page Six at the time that the out-of-control star was "six inches away" from Rocky's face, yelling, 'Who are you?
Brooks said Depp continued his belligerent behavior until bodyguards removed him from the set.
Rocky, who claims Johnny smelled of alcohol, is seeking unspecified damages. The movie is set to open September 7 from Global Road Entertainment.
When Brooks returned to the set three days later, producer Miriam Segal allegedly wanted him to sign a declaration stating that he would not sue the production team.
Brooks is suing for assault and battery, infliction of emotional distress and negligence, among other things.
The lawsuit is just the latest setback for Depp, whose financial woes have played out in the media amid multiple court cases.