When Bill Murray replaced Chevy Chase on “Saturday Night Live” in 1977, the move did not go over well with audiences. In fact, Murray was initially considered such a dull, awkward bomb that he appeared in a fake telethon sketch asking viewers to send in money to help him be funny.

If he stars in many more projects like “Broken Flowers,” he’s going to need to resurrect that fundraising scheme.

Despite occupying nearly every scene, Murray is a virtual nonpresence in Jim Jarmusch’s latest puzzler. Unlike “Lost in Translation,” in which the comedian brought humor, depth and a world-weary charisma to the part, he all but sleepwalks through Jarmusch’s canvas. The feature also offers Murray his least funny role next to “Garfield.”

The movie exists as an exercise for the disconnected actor to underreact to things: a conversation, an argument, a punch to the face. Whether he’s miscast or misdirected becomes the real debate.

At least writer-director Jarmusch’s (“Coffee and Cigarettes”) premise shows promise by combining a mystery with a road trip.

Bill Murray portrays a former ladies man who embarks on a quest to contact his former girlfriends in Broken

Murray stars as Don Johnston, a former Don Juan now basking in the retired malaise of a successful career in computers.

As the film begins, his young French girlfriend is leaving him (much in the same way Murray’s comedy “Stripes” opens), explaining that she feels “like your mistress, except you’re not even married.”

He then receives an unsigned letter claiming to be from an ex-lover of two decades ago that reveals the existence of a 19-year-old son. The woman discloses the boy may come looking for his father.

Don’s neighbor Winston (Jeffrey Wright) helps do some detective work and comes up with a list of current addresses for Don’s past flames from that era. So with MapQuest directions in hand, Don embarks on a journey to find the potential mother of his potential child.

The reason the picture ultimately feels hollow is that Murray exhibits no traits that would make him irresistible to women, which is supposed to be the very essence of his character. He’s a humorless dud who sits around drinking champagne while wearing track suits, like some mobster under house arrest.

The film contains a running joke that individuals usually smirk when they hear Don Johnston’s name (he always emphasizes, “It’s with a ‘T'”). But the real “Miami Vice” star would probably make a better fit in this role, because at least the audience could envision him as a former ladies man.

This central casting choice serves as a Catch-22 for the veteran Jarmusch. Although his leading man is all wrong, Murray’s very involvement ensures the movie gets a wide release in multiplexes – a rarity for the indie director. (It’s still scheduled at the art house in Lawrence, however.)

The rest of the cast also is populated with Oscar nominees who make little impression. As Don hunts down his past lovers, Sharon Stone, Jessica Lange and Tilda Swinton all show up as increasingly harder-to-believe characters. Then there are flirtations involving a a fresh crop of teens and twentysomethings, such as Chloe Sevigny and Alexis Dziena, which leads to an extraordinarily exploitative and improbable nude scene.

Bill Murray and Sharon Stone star in Broken

Jarmusch proves better-skilled at establishing a mood than verisimilitude. Like Stanley Kubrick, he’s brave enough to let shots linger past their normal editing points. The filmmaker also masterfully uses atypical music (The Greenhornes, Mulatu Astatke) in recurring bites to create a haunting backdrop.

Despite the pivotal flaw, “Broken Flowers” remains watchable because the story is seductively enigmatic. Jarmusch peppers his landscape with clues – coincidental names, the color pink, basketball goals – that all seem to be leading to a connection. Whether they do is open to interpretation.

It’s possible “Broken Flowers” may offer more dramatic weight on a second viewing. Or it’s possible that the movie (and Murray) may be even more annoying.