It has become customary in the USA for presidential candidates to release their returns, which offer a window into their personal finances and business dealings. The subpoena calls for financial and tax records of a number of entities and individuals, including those of President Trump.
Writing on Twitter, President Trump has condemned the request for his tax returns for eight years.
The stakes of the legal fight have only increased with the Democrats starting a formal impeachment inquiry.
Grand jury proceedings and records in NY are secret.
NY attorney Barry Barnett told The Epoch Times that the judge's ruling signified a "very partisan fight".
On Monday, a federal judge at the court in New York City rejected Trump's position on the matter, saying he could not "square a vision of presidential immunity that would place the President above the law".
"This court can not endorse such a categorical and limitless assertion of presidential immunity from judicial process", Mr Marrero wrote.
Harry Sandick, a former federal prosecutor and partner at Patterson, Belknap, Webb & Tyler in NY, said the ruling was clear.
Lawyers for US President Donald Trump may have overplayed their hand. That means the returns are unlikely to be turned over immediately. He has sued the investigators and the companies they had subpoenaed, including Mazars and two of Trump's banks. Mazars took no position in the case. The request is in connection with an investigation into the payment of hush money to two women who claimed they had had affairs with the president. The Trump Organization later reimbursed Cohen.
Cohen is now serving time in federal prison for campaign finance violations related to the payments.
A previous Web summary of this story incorrectly said a federal appeals court issued a ruling in the case. Justice Department policy, however, has always been that sitting presidents can not be charged criminally, and impeachment is the only way to address potential wrongdoing. Vance has until October 17 to respond.
The memos, he said, have attained an unwarranted popular acceptance, "as if their conclusion were inscribed on Constitutional tablets so etched by the Supreme Court". The judge said the president was entitled to no such "protective shield". If the tax records expose such payments, I think Trump is in real trouble.
The judge, however, made clear that if the appeals court disagreed with that finding, Trump should lose.
The developments escalate the president's battle to keep his finances under wraps, despite having promised during his 2016 White House run that he would disclose his tax returns.
The judge rejected arguments by the president's lawyers that total immunity protects him while in office.
But they haven't been tested by a court, and a state prosecutor like Vance may disagree with the analysis in the memos and try to charge Trump.
A spokesman for Vance declined to comment.
A Justice Department lawyer on Monday asked the appeals court to give the department sufficient time to weigh in, saying the issues involved were novel and raised weighty constitutional concerns.
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