Mr Brafman also said he would investigate what he said had been "perjury" before the grand jury which indicted Mr Weinstein, as well as the conduct of a NY police officer who had worked on the case.
"This is not about suggesting that a woman who comes forward should not be believed", Brafman said in a press conference. Brafman has called the charges against Weinstein a product of political pressure amid the (hash) MeToo outcry.
In a statement, a spokesperson for The New Yorker said that the magazine stands by their reporting and fact-checking process, adding that "Any assertion by lawyers for Harvey Weinstein that The New Yorker had information that contradicted Lucia Evans's account is patently incorrect".
An attorney for the Harvey Weinstein accuser whose case has been dropped says it does not "invalidate the truth of her claims".
US-based tabloid website TMZ reported last week that a casting director claimed Evans once told her she performed oral sex on Weinstein to gain an acting role.
During the Thursday hearing, the prosecutors agreed to drop charges relating to an alleged sexual assault.
Prosecutors said in a letter unsealed Thursday they learned weeks ago that a woman who was with Evans the night she met Weinstein at a restaurant had given a police detective a contradictory account of what happened, but that the detective had urged her to keep quiet, telling her "less is more".
Weinstein, who has denied all allegations of non-consensual sex, still faces charges over allegations he raped an unidentified woman in his hotel room in 2013 and performed a forcible sex act on a different woman in 2006.
Carrie Goldberg, an attorney for Evans, spoke to reporters outside the court in lower Manhattan following the dismissal.
Weinstein's legal team argued in court papers that prosecutors hadn't properly identified the day on which Evans alleged she had been assaulted. Weinstein had promised to get her an acting job if she agreed to perform oral sex, and she agreed, it said.
A lawyer for Evans said they were disappointed by the decision, saying in a statement the district attorney abandoned their client. "It only speaks volumes about the Manhattan DA's office and its mishandling of my client's case".
The accusations led to the #MeToo movement in which hundreds of women publicly accuse powerful men in business, politics and entertainment of sexual harassment and abuse. "The evidence shows that the criminal case against him is strong".
Although Brafman said he has "great respect" for the D.A.'s office, "I have deep regret that the thoroughness of the investigation did not prevent them from charging Mr. Weinstein with a crime he did not commit". At the time, Vance cited a lack of supporting evidence, despite the existence of a clandestinely made recording of Weinstein discussing the episode with the woman.
Weinstein's bond was set at $10 million and he is required to wear a GPS monitoring system and is only allowed to travel within NY state or CT.