The House Democrat charged with obtaining President Donald Trump’s tax returns indicated he’s going to sue, rather than issue a subpoena, in the next battle to obtain the president’s records.

“They don’t seem to be responding to a lot of subpoenas around here,” House Ways and Means Chairman Richard Neal told reporters late May 7. “I did say this was going to end up in the courts, right? And that’s where it’s headed.”

Treasury Secretary Steven Mnuchin on May 6...