The construction worker who accused a Brooklyn cop of stealing $1,300 from his pocket during a search was actually carrying just $62 — and it was all properly vouchered, the NYPD said Thursday.

Officer William Montemarino, a 22-year veteran, was cleared of any wrongdoing by Internal Affairs after the Sept. 22 incident outside the Surfside Gardens housing project, sources told The Post.

A week later, Lamard Joye, 35, and his lawyer, Robert Marinelli, went to the Brooklyn District Attorney’s Office and claimed the cop had taken $1,300.

On Thursday, Patrolmen’s Benevolent Association President Pat Lynch defended the officer, saying: “It is time for people to start giving the cops the benefit of the doubt.

“In reality this was someone who fit the description of a man with a gun and all his property including money and cellphone were vouchered,” Lynch said.

Marinelli gave them a canceled check and withdrawal slips as proof — but admitted to The Post that those documents are from between five and seven days prior to the scuffle.

“Just because somebody cashes a check and has a bank record, that doesn’t mean they still have the cash on them a week later,” a law enforcement source said.

IAB launched a second investigation Thursday, after Marinelli went to the media with a cellphone video that shows Montemarino holding cash he took from Joye’s pocket — before pepper-spraying Joye when he mouthed off.

The officer has not been suspended and remains on patrol, the sources said.

Brooklyn DA Ken Thompson’s office is also investigating.

At least five officers rushed to the West 31st Street housing complex that night in response to a 911 call of a gun-toting man in a black hoodie and black pants. A large crowd, including Joye, interfered with the cops.

“The crowd was ordered to disperse, but one of the males in the group attempted to prevent the officer from issuing [another] suspect two summonses, for disorderly conduct and unlawful possession of marijuana,” an NYPD spokeswoman said in a statement.

Joye was frisked against a fence, and Montemarino removed his cellphone and $62 in cash, the statement said. Joye — who has an open warrant for driving without a license — and his sister were then pepper-sprayed by Montemarino.

He ran off before cops could arrest him.

“The officer returned to the precinct and vouchered the suspect’s cellphone and $62. The suspect never returned to the precinct to obtain his property,” said the NYPD.

“He was taking his girl out [on a vacation] the next day,” Joye’s cousin and the witness who took the video, Shannal Mitchell, 28, told The Post on Thursday.

“He wanted to make sure he had [the money] out before that day because they were leaving early in the morning,” Mitchell added.

“They just pepper-sprayed him, took his money, his phone, and that was it.”

Additional reporting by Dana Sauchelli, Ben Feuerherd and Josh Saul