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ALBANY — New York State lawmakers on Wednesday gave their final approval to a bill that would clear a path for Congress to obtain President Trump’s state tax returns, injecting another element into a tortuous battle over the president’s refusal to release his taxes.

The bill, which is expected to be signed by Gov. Andrew M. Cuomo, a third-term Democrat and regular critic of Mr. Trump’s policies and behavior, will authorize state tax officials to release the president’s state returns to any one of three congressional committees.

The returns — filed in New York, the president’s home state and business headquarters — would likely contain much of the same information as the contested federal returns, though it remained unclear whether those congressional committees would use such new power in their investigations.

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.