The crazy eyes and idiosyncratic drawl of Woody Harrelson are enough to carry the dirty cop study “Rampart,” but even such powers as those can’t make engaging this weary LA noir.Without Harrelson’s inherent intrigue, the heavy-handed provocations of “Rampart” would be difficult to suffer. But his intense and committed performance keeps Oren Moverman’s film moving, even while the grim and overdone story wallows affectedly.

Among the dirty cops of movies – Harvey Keitel in “Bad Lieutenant,” Denzel Washington in “Training Day” – Harrelson’s LAPD Officer Dave Brown is particularly ugly. He’s nicknamed “Date Rape Dave,” a moniker he came by from killing a serial date rapist years ago. The name may hint of Brown’s most decent side (a protector of women) but it also serves as a frightening warning.

“Rampart” is set in 1999 Los Angeles and its title refers to a notoriously scandal-plagued police division. The film, which Moverman adapted from crime fiction writer James Ellroy’s novel (both are credited for the screenplay), doesn’t try to analyze what led to a corrupt division, but rather the specific formation of a badge-wearing monster.

“How do we solve a problem like Dave Brown?” asks police attorney Joan Confrey (Sigourney Weaver).

By then, we’ve already seen Brown lament “Rodney King wannabes,” abuse a handcuffed suspect and beat to a pulp a man who had the misfortune of colliding with Brown’s cruiser. That incident is caught on camera and replayed on the evening news, sparking protests and an investigation.

“This used to be a glorious soldiers’ department,” sneers Brown to a mixed-race female officer. “And now it’s ... you.”

Nice guy, right? At home, we see a softer, complicated side. Brown has two ex-wives (Cynthia Nixon and Anne Heche, both looking lost) who are sisters and neighbors, with whom he has a teenage daughter (Brie Larson) and a younger daughter (Sammy Boyarsky). It’s an incredulous arrangement and we can only be glad, for basic clarity, when the younger girl sweetly asks her father if she’s inbred. (He laughs and tells her she isn’t and that she’s “native.”)

The bizarre domestic situation aside, Brown’s face genuinely glows around his daughters, surely his only possible pathway to salvation.

But Brown is in a self-destructive tailspin: acting out violently, desperate for departmental cover (Ned Beatty plays a sinister LAPD retiree) and picking up women easily. He approaches one (Robin Wright) at a bar by commenting on her “litigator eyes.” Their relationship forms as one based on mutual self-loathing, and Wright is captivating in every moment.

How does he live with himself? Quite self-assuredly, actually. The most interesting quality of Brown is how hyper-literate he is.

He might curse all manner of LA citizens as “scum,” but, when confronted by superiors or lawyers (Steve Buscemi makes a cameo as one), he responds with a torrent of dubious legalese and moral equivocation. He shrouds his behavior in a labyrinth of caginess, defending himself as a Vietnam vet and a true-blue of the old guard.

This is Moverman’s second stab at direction following 2009’s “The Messenger,” which also fitted the famously liberal Harrelson in a uniform (as a soldier whose duty is to inform the families of the fallen).

With cinematographer Bobby Bukowski, Moverman’s jerky, handheld camera keeps LA always in the background. The first shot is a profile of Brown driving, smoking and stoic behind sunglasses, while Los Angeles passes behind as mere backdrop. The protests over his beating, we never see, just hear. Instead of leading toward understanding, “Rampart” remains a dirty cop caricature, more a complaint than a story.