Democrats in Washington have been unable to obtain Mr. Trump’s federal returns. The Ways and Means Committee has unsuccessfully sought six years of the president’s personal and business tax returns, and last week the House of Representatives sued the Treasury Department and the I.R.S. to try to force them to release the returns.

The state tax documents from New York — the president’s home state and business headquarters — would likely contain much of the same information as the contested federal returns, tax experts say.

Mr. Cuomo, a third-term Democrat and frequent critic of Mr. Trump, said that signing the bill would help Congress “fulfill its Constitutional responsibilities, strengthen our democratic system and ensure that no one is above the law.”

The Legislature had passed the measure in late May; Dani Lever, Mr. Cuomo’s communications director, said that the six-week delay in signing the bill was because the governor’s office needed to do a diligent analysis of the legislation and its amendments.

“Any responsible government would thoroughly review this bill, just as we will with more than 930 bills passed this session,” Ms. Lever said, noting “how high the stakes are of this particular legislation.”

Mr. Trump defied longstanding tradition by refusing to release his tax returns as a presidential candidate in 2016, and has continued to decline to share the documents, citing federal audits of his taxes. Mr. Trump has previously said that he is ready to take the fight over his federal tax returns to the United States Supreme Court.

The White House on Monday had no comment on Mr. Cuomo’s signing of the bill.

Steven M. Rosenthal, a senior fellow at the Urban-Brookings Tax Policy Center, said that there were limits built into the new New York law on revealing federal tax details, but that a state return could still illuminate things like the president’s adjusted gross income.