This Aug. 1, 2018, file photo shows Rudy Giuliani, an attorney for President Donald Trump, in Portsmouth, N.H. As Giuliani was pushing Ukrainian officials in the spring of 2019 to investigate one of Donald Trump’s main political rivals, a group of individuals with ties to the president and his personal lawyer were also active in the former Soviet Republic. Credit: Charles Krupa | AP

By now it’s clear that Rudy Giuliani was the driving force behind the Ukraine scandal engulfing President Donald Trump’s administration. But he refuses to testify before the House investigation of the matter, and (for now) has the support of the White House.

That leaves the Senate. Senate Republicans have offered Giuliani the opportunity to tell his story in a friendly partisan environment, and he says he welcomes it. They now need to insist that Giuliani put up or shut up: Either testify before the Judiciary Committee or face a formal investigation by Foreign Relations Committee.

Giuliani has a lot to tell. His Ukrainian escapades began as an attempt to prove that it was Hillary Clinton, not Trump, who got foreign help in 2016. Along the way, he expanded his brief to include discrediting Special Counsel Robert Mueller’s investigation and report. But the story Giuliani found — fed to him by Ukrainian officials who knew precisely what they were doing — was too good for him to resist: Not only was the Mueller investigation a hoax, it was part of a larger conspiracy.

This conspiracy had three goals. First, it sought to defeat Trump in 2016 by manipulating the election. Second, it sought to undermine his presidency by feeding information about his allies, in particular former campaign manager Paul Manafort, to Mueller’s investigation. Third, it sought to defeat Trump in 2020 by suppressing a damaging investigation into his chief rival, former Vice President Joe Biden.

To be clear: These allegations are flimsy at best and bogus at worst. Giuliani has repeatedly claimed that he has documentary evidence in support of them. If he does, it was almost certainly produced by a corrupt Ukrainian prosecutor attempting to save his job and promote his interests.

Other Trump advisers have questioned Giuliani’s “evidence.” Homeland Security Adviser Thomas Bossert tried repeatedly to counter Giuliani’s narrative until he was removed. National Security Adviser John Bolton then took over the role, but eventually found himself on the outs. At every turn, the pros lost ground and Giuliani gained. Even now, as Giuliani’s associates in Ukraine face fraud and conspiracy charges, Trump remains reluctant to cut him loose.

Since the executive branch has tried and failed to contain Trump’s wayward personal attorney, it’s up to the legislative branch. Practically speaking, that means the Senate.

The White House has refused to cooperate with the impeachment inquiry in the Democrat-controlled House. In the Senate, Republicans are in control. Trump and Giuliani may think they are more likely to get a fair hearing.

Even better, at least from Trump’s perspective: Impeachment need not be the issue. Public testimony shows that Giuliani, an unconfirmed presidential adviser, has undermined the diplomatic and national security efforts of Senate-confirmed executive-branch appointees. The Senate has a duty to investigate this breach of its advise-and-consent powers.

If Giuliani refuses to come forward and tell his story to the Senate, then it should open an investigation of the State Department’s and the White House’s diplomatic efforts. One way or another, the Senate needs to send a clear message: Those who claim to be acting on behalf of the American government must be held accountable to the American public.

Karl W. Smith is a former assistant professor of economics at the University of North Carolina’s school of government and founder of the blog Modeled Behavior.