Mug shots of John Wojtowicz after the bank robbery that inspired “Dog Day Afternoon.” His complicated story is told in the darkly humorous documentary “Dog.” (Drafthouse Films/Cinedigm)

The T. Rex song “Life Is Strange,” which ushers in the closing credits of “The Dog,” feels like a giant understatement, based on what has come before it. The fascinating and, at times, very funny documentary portrait of the late John Wojtowicz (1945-2006), whose 1972 attempted bank robbery inspired the film “Dog Day Afternoon,” also puts that narrative feature to shame. Sidney Lumet’s 1975 drama about an everyday Joe (Al Pacino) who turns to crime to bankroll his male lover’s sex-change operation seems positively pedestrian compared to the unyielding oddness of Wojtowicz’s true-life saga.

The tale spun by “The Dog” comes courtesy of its titular subject, whose nickname refers both to the fictionalized film he inspired and, to hear Wojtowicz tell it, his only partly tongue-in-cheek characterization of himself as a “pervert.”

It’s not the derogatory epithet of a self-loathing gay man that it sounds like. Far from it. In numerous interviews that careen from profane braggadocio to tender reminiscence, the lustily bisexual Wojto­wicz comes across as almost bizarrely self-satisfied. This, despite the fact that several other interviewees — including Wojtowicz’s ex-wife, Carmen, whom he calls his “female wife,” and the transsexual object of his criminal affection, Liz Eden — allude to him as having wreaked havoc on their lives.

Wojtowicz’s path to notoriety was littered with unhappiness, despite the fact that Eden, who was born Ernie Aron, ultimately got the operation she desired. That was no thanks to the robbery, which was foiled, resulting in the death of Wojtowicz’s accomplice, Sal Naturale, and Wojtowicz’s imprisonment from 1973 to 1978. Rather, Eden’s sex-reassignment surgery was financed by proceeds from the 1975 film. Throughout her life, however, she struggled to overcome the pull of prostitution and a precarious mental state, dying of AIDS complications in 1987.

Despite these sad outcomes, which inspire one interview subject to call Wojto­wicz a loser, the man himself maintains an alarmingly sunny outlook throughout the film, joking and cursing in a thick New York accent, even as he is ravaged by cancer toward the end of the documentary. As a tour guide, he’s highly entertaining, despite some obvious moral blind spots.

This attitude of his brightens the film, while also adding a discordant note that paradoxically enriches and complicates the tale. Filmmakers Allison Berg and Frank Keraudren also mix in a mini-history of the gay liberation movement and the early days of marriage-equity activism. Wojtowicz refers to himself as having married Eden, though he was not technically divorced from his first wife. A relationship with a third “spouse” — Wojtowicz’s jailhouse lawyer, George Heath — is also discussed in depth, as is Wojtowicz’s surprisingly sweet relationship with his developmentally disabled older brother, Tony.

In addition to “pervert” — which Wojtowicz makes sound like a badge of honor — the film offers many other seemingly contradictory assessments of Wojtowicz, mainly from his own mouth: troll, Goldwater Republican, McCarthy peacenik, crazy man, crook, romantic. He was all of those things and more, as “The Dog” makes vividly obvious.

★ ★ ★

Unrated. At the West End Cinema. Contains frequent obscenity, discussion of sexual matters and brief nudity. 100 minutes.

West End will offer daily screenings of “Dog Day Afternoon” as a companion to the documentary.