The returns — filed in New York, the president’s home state and site of his Trump Tower headquarters in Manhattan — are likely to contain much of the same information as his federal tax returns, which the Trump administration has refused to hand over to Congress.

The Legislature’s actions put the state in a bit of uncharted legal territory; Mr. Trump has said that he is ready to take the fight over his federal tax returns to the Supreme Court, and it seems likely that he would seek to contest New York’s maneuver.

Even so, among the Democrats who have long been frustrated over the president’s refusal to release his returns, the Legislature’s action was cast as a victory for states’ rights and the often-unsung power of their lawmakers.

“It’s a matter of New York’s prerogative,” said Senator Brad Hoylman, the Manhattan Democrat who sponsored the bill in his chamber. “We have a unique responsibility and role in this constitutional standoff.”

In Washington, two congressional committees issued subpoenas last month to Deutsche Bank, the president’s primary lender over the last two decades, and Capital One, where Mr. Trump keeps some of his money. The subpoenas sought decades of personal and corporate financial records, including any documents related to possible suspicious activities detected in Mr. Trump’s personal and business accounts.

Mr. Trump, his company and his three eldest children — Donald Jr., Eric and Ivanka — filed a lawsuit on April 29 to block Deutsche Bank and Capital One from complying with the subpoenas.