Connecting an actor’s onscreen personality with his or her offscreen reality tends to be a dicey proposition. But in “ Faye ,” an addictive and essential portrait of Faye Dunaway , it turns out to be the right thing to do. Dunaway, now in her early 80s, is interviewed throughout this HBO documentary, and there’s a knowing snap to her self-reflections that grabs you.

Seated on a couch in her New York apartment, she starts off by chastising someone for bringing her water in a bottle instead of a glass — a sign that the movie is going to have fun with what a diva she is. As “Faye” presents it, Dunaway was too volcanic and troubled a personality not to pour herself into her roles. That’s part of what made her great.

Yet the film also wants to cue us to the gossipy and reductive way that this kind of thinking has too often been applied to her. Dunaway, by her own admission, was demanding, perfectionistic, and nothing short of obsessive in the pursuit of acting — in other words, she was “difficult” because she possessed many of the qualities that male actors have been celebrated for, and are certainly more easily forgiven for. In “Faye,” we see a clip of the ancient Bette Davis on “The Tonight Show,” asked to name the star she’d least want to work with again.

She blurts out Dunaway’s name, then says that everyone in Hollywood would say the same thing. Talk about projection! But the talk-show audience has quite a chortle. Yet the first thing to say .