The request by the House Committee on Ways and Means "lacks a legitimate objective", meaning the US Treasury is not authorised to release tax filings by Trump and his businesses, Mnuchin said in a letter to the committee's chairman.
"I am informing you now that the department may not lawfully fulfill the committee's request", he said.
Democrats initially directed their request to IRS Commissioner Charles Rettig, the only person with the legal authority to turn over the returns, but Mnuchin has interceded twice in the matter, citing his role overseeing the federal tax collector.
"As you recognized, the Committee's request is unprecedented, and it presents serious constitutional questions, the resolution of which may have lasting consequences for all taxpayers", added Mnuchin.
Mnuchin said Monday he had made his decision in consultation with the US Department of Justice.
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The request for Mr. Trump's taxes is the latest instance of the Trump administration rebuffing congressional oversight efforts.
The state tax returns can only be released under Hoylman's legislation if requested by any of three committees: The House Ways and Means Committee; the Senate Finance Committee; or the Joint Committee on Taxation.
The statute says that the secretary of the Treasury "shall furnish" it. While Congress does have broad authority to investigate the Executive Branch, that authority is not unlimited and this is one of the cases where it must be able to articulate why it needs to see the returns beyond merely stating "we want to see them". New York's proposed law wouldn't authorize the discloser of Trump's returns in any of the years described in the Times report.
After Neal first issued the request, the Trump Administration immediately suggested that it would fail to comply with the request, with Mnuchin blowing off two deadlines imposed by Neal to hand over the tax information.
Gov. Andrew Cuomo, a Democrat, has said he supports legislation allowing the president's tax returns to be made public, but only if it also applies to all state lawmakers and statewide elected officials in NY.
"Whether it is refusing to sit down in an interview with Mueller or whether it is constantly obstructing justice by trying to stop testimonies and stop people from cooperating, whether it is filing a lawsuit, he obviously has something to hide", House Financial Services Committee Chairwoman Maxine Waters said last week. "We're not going anywhere", he said.