PARK CITY, Utah — When Zac Efron sang “Breaking Free” in 2006’s “High School Musical,” little did we know he meant out of police custody. But 13 years later the actor has gone from playing a singing, basketballing hunk to a murderous psychopath with a penchant for running from the cops. That’s right — Efron is doing his finest acting ever as serial killer Ted Bundy.

If only his movie “Extremely Wicked, Shockingly Evil and Vile,” which premiered Saturday at the Sundance Film Festival, was as good as he is in it.

Unfortunately the hotly anticipated drama, directed by documentarian Joe Berlinger, provides only a surface-level look at who Bundy was and the atrocities he committed. “Extremely Wicked” is far more concerned with how he hid his hobby from girlfriend Elizabeth Kloepfer, and why hordes of women believed in and obsessed over him during his trial. When you cast Efron, it’s not hard to guess the reason.

The movie begins with Bundy meeting Kloepfer (Lily Collins) at a bar in Washington state in 1974, and follows their courtship in the months after. He’s sweet, sexy and loving — and the definition of “too good to be be true.” While we witness him at home making breakfast in an apron, or at law school in Utah, he’s spending his evenings killing at least 30 young women.

We see almost none of his crimes — “Dexter,” this is not — but instead experience the events through newspaper headlines, as the press becomes increasingly obsessed with the story of the missing college coeds. Bundy is arrested while driving in 1975 because he matches the description of a man wearing a sling driving a Volkswagen Beetle witnessed near the crime scenes. And then the film turns into a courtroom drama.

Much of the film is his highly theatrical trial — made even more so by the fantastic casting of John Malkovich as the judge — and his habit of evading the cops. At one point, he escapes and runs off to Florida, where yet more women are killed. But, again, we don’t see any of those horrors. Shielding us from Bundy’s misdeeds makes him disconcertingly likable. And “Extremely Wicked” is, for better or worse, a very funny movie.

Berlinger’s aim, it seems, is to cast doubt on whether or not Bundy actually murdered anybody until the very end of the movie to maintain suspense. Good luck, Joe! This guy wasn’t OJ Simpson — Bundy confessed, got the chair and kept the decapitated heads of some of his victims. The world is well aware that he did it.

The director does manage to give his first narrative feature a cool, washed-out look, and he coaxes some terrific performances from his actors. Collins’ Kloepfer is wracked by doubt and confusion over Bundy’s guilt, but you can also discern that there is one big secret in her life.

However, “Extremely Vile,” from start to finish, belongs to Mr. High School Musi-Kill. Efron certainly had his doubters when he was announced in this role — blood and guts are not really his bread and butter — but he shows them by brilliantly warping his usual charisma and good looks into something so sinister and loony. His Bundy has crazy eyes and a heart of ice, and makes us wish he’d star in less “Neighbors” films and more dramas.

Perhaps he could play Ted Bundy in a much better mini-series.