If you made up the story of Burt Puglich and Linda Riss, it would probably be dismissed as so implausible that people would never believe it. But as it happens, the tale of the lawyer who becomes so obsessed with a beautiful young woman that he hires someone literally to deface her when she dumps him and then, having served prison time for the crime, marries her, is—believe it or not, as they used to say—all true. And documentarian Dan Klores has done a nifty job of bringing it to the screen in the aptly-titled “Crazy Love.”

Burt Pugach was a crafty personal injury lawyer who made big bucks for himself and his clients, but hardly a he-man type, when he spied the lovely Riss in a New York park and was immediately smitten with her. The pair soon became a fixture on the New York nightclub circuit despite her family’s doubts about the older man. Those doubts were proven correct when it came out that Burt was hiding the fact that he was not only married but had a disabled daughter. And when Linda broke it off with him, he hired an inept hit-man to attack her with acid at her doorstep, leaving her badly disfigured and almost blind.

That story is melodramatic enough, but the level is ratcheted up by what followed: Pugach became a jailhouse lawyer behind bars, and after his release announced that he was still in love with Riss, whose fiance had broken off his engagement with her after the attack, leaving her alone and forlorn. The two got together again and continue as a couple to the present day, despite charges of infidelity that have been raised against Burt since.

The structure that Klores has imposed on this wild scenario isn’t ideally clear or perfectly paced, but using stills, newspaper stories, footage from news programs and talk shows, and abundant interviews—with friends, journalists like Jimmy Breslin, observers, family members and, most astonishingly Burt and Linda themselves (as well as film of them in their daily lives)—he captures the sheer weirdness of the tale without turning it into sleazy sensationalism. It’s especially intriguing to watch Pugach’s refusing to admit any real wrongdoing and Riss coming across simultaneously as pathetic and combative. In an era of trashy tabloid journalism, “Crazy Love” raises the bar, turning what’s really a sordid story into a perversely fascinating romance involving people who are damaged both psychologically and physically.