President Donald Trump asked a federal judge for an emergency order keeping House Democrats from getting—or even asking for—his New York State tax returns.

One day after the president sued to block the House Ways and Means Committee from obtaining those records under a newly enacted New York State law, he petitioned the court to stifle any such request before it’s made by Committee Chairman Richard Neal, a Massachusetts Democrat.

Neal hasn’t committed to asking for the returns. They were placed within reach by the TRUST Act, a measure signed into law by Governor Andrew Cuomo earlier this month. It...