Moreover, Judge Weinstein suggested that giving a jury the question of whether the department has permitted widespread police perjury could prompt important reforms. “It may indicate the need for more careful tracking of individual police officer’s litigation history and a more effective discipline policy to avoid repeated lying by a number of officers,” his ruling stated.

Judge Weinstein’s decision came in a routine case, involving a lawsuit brought by a 59-year-old bodega cashier, Hector Cordero, who was arrested on Oct. 24, 2014, and charged with drug dealing on slight evidence. Plainclothes officers from the 83rd Precinct in Bushwick, Brooklyn, claimed to have seen a man walk out of the bodega where Mr. Cordero worked and sell two bags of drugs to a man waiting outside. The dealer then re-entered the bodega, according to the police account. The officers arrested the man they described as the purchaser, but there was some initial difficulty finding the dealer, according to the officers’ accounts, which were summarized in the decision.

Officers who initially went inside the bodega left after being unable to identify the suspect, according to the court decision handed down Tuesday. A little later, however, officers arrest Mr. Cordero, the cashier, and accused him of being the dealer.

Mr. Cordero, who was a police officer in the Dominican Republic before immigrating to the United States, had no criminal record. A co-worker testified that he could not have been the drug dealer, as he was in the store during the period in question. No drugs were found on him during a strip search that Mr. Cordero said involved him taking off his underwear. Eventually the charges against him were dropped.

In his lawsuit against the police, Mr. Cordero accused the officers of arresting him because they wanted to make the overtime pay that ensued from an arrest near the end of their shift. In his decision, Judge Weinstein noted that one of the officers involved in arresting Mr. Cordero, Hugo Hugasian, had previously been suspended from the force for 60 days and required to pay $1,203.74 in restitution for claiming overtime pay for hours he did not work. And Judge Weinstein noted that officers were paid at least 22 hours of overtime for the arrests of Mr. Cordero and the other man outside the bodega.