Mr. Trump, who is from New York and whose business is still headquartered here, has steadfastly refused to release his federal tax returns. And while Republicans suggested that the attempts by the Democrat-led Legislature were partisan, both Mr. Hoylman and Mr. Buchwald defended their bills, saying that voters had a right to know about Mr. Trump’s personal and business finances.

“Making sure that the public has information about the man currently in the White House is something that I feel is incumbent upon us to make sure is released,” Mr. Buchwald said, adding, “There’s a copy of President Trump’s New York State tax returns right here in New York State, in an office somewhere.”

Both lawmakers said that the urgency of their bills had increased since last week, after a request from the House Ways and Means Committee chairman, Representative Richard E. Neal of Massachusetts, to release six years of Mr. Trump’s federal returns by April 10. The I.R.S. and the Treasury Department in Washington are still deciding whether to comply with that request, but on Sunday, the White House chief of staff, Mick Mulvaney, said that Democrats would “never” see the president’s tax returns.

Andrew Sidamon-Eristoff, a former commissioner of taxation and finance under Gov. George E. Pataki, said that Mr. Hoylman’s bill would “generate furious and lengthy litigation” if passed, because of federal laws protecting tax information.

“The I.R.S. and others will likely argue that most New York return information is based on protected federal return information,” Mr. Sidamon-Eristoff said. “Disaggregating the information will be a major practical challenge, if not impossible.”

In January, Mr. Cuomo had proposed a plan to have all candidates for statewide and legislative office release several years worth of returns, but the measure did not advance. Mr. Cuomo allows reporters to see his taxes every April, but does not allow copies to be made.

The bill introduced on Monday by Mr. Hoylman would amend current state laws that generally prohibit such private tax information from being released, and would cover a broad range of filings, including personal income taxes, corporation taxes and real estate transfer taxes. Under it, the chairman of any of three congressional committees — the Senate Finance Committee; the House Ways and Means Committee; and the Joint Committee on Taxation — could request tax returns from the New York tax department, which would be authorized to release the information.