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ALBANY — As the standoff over President Trump’s federal tax returns deepens in Washington, New York State lawmakers say they intend to advance a bill on Wednesday to allow congressional committees to see Mr. Trump’s New York State returns.

State Senator Brad Hoylman, a Manhattan Democrat, confirmed on Tuesday that the State Senate had enough votes to ensure passage of a bill allowing the commissioner of the New York Department of Taxation and Finance to release any state tax return requested by a leader of one of three congressional committees for any “specified and legitimate legislative purpose.”

A tax return from New York — the headquarters of the president’s business empire and his home state — could contain much of the same financial information as a federal return, which Mr. Trump has steadfastly refused to release. On Monday, the Treasury Department denied a request from House Democrats for six years of the president’s federal returns, setting up a likely court battle that could reach the Supreme Court.

“The news of yesterday makes New York’s role even more crucial,” Mr. Hoylman said. He has described his bill as “assisting Congress in its oversight role.”