In particular, the state prosecutors are examining whether the company falsely accounted for the reimbursements as a legal expense. In New York, filing a false business record can be a crime.

But it becomes a felony only if prosecutors can prove that the false filing was made to commit or conceal another crime, such as tax violations or bank fraud. The tax returns and other documents sought from Mazars could shed light on whether any state laws were broken. Such subpoenas also routinely request related documents in connection with the returns.

Democrats have insisted for years that Mr. Trump release his tax returns, which every modern presidential nominee has done before him. They contend that the president may be trying to conceal details of his actual financial worth, the source of his wealth and possible conflicts of interest involving his business partners.

Congressional Democrats have taken an aggressive approach, subpoenaing six years of Mr. Trump’s tax returns from the Treasury Department, as well as personal and corporate financial records from Deutsche Bank, Capital One and Mazars USA.

The president has fought back to keep his finances under wraps, challenging the subpoenas in federal court. He has also sued to block a New York State law, passed this year, that authorized state officials to provide his state tax returns in response to certain congressional inquiries. By tying up the requests in court, Mr. Trump’s team has made it diminishingly likely that Democrats in Washington will get the chance to review them before the election next year.

But it may be more difficult to fend off a subpoena in a criminal investigation with a sitting grand jury, as there is in Manhattan. It is possible the Trump Organization could try to negotiate with the district attorney’s office to narrow the scope of the subpoena.

Jay Sekulow, a lawyer for Mr. Trump, and Marc L. Mukasey, a lawyer for the Trump Organization, both declined to comment.