Adding to the weirdness of the entire picture, but especially this scene, the '60s rock band The Zombies are playing a performance on the bar television. A strange choice of product integration, but the jangly, Brit pop band lends a disquieting undercurrent of youthful jubilee to Ann's rather horrifying tales of childhood (that doll funeral--eek!)
The fact that the bartender changes the channel from a news report on the missing girl to the rock performance underlines the casual dismissal of almost all involved (and from Preminger himself) in actually ever finding the girl. When the mystery is finally concluded, Bunny Lake is treated with indifference. The last twenty minutes or so shifts entirely from Newhouse & the police investigating to Ann taking up the mantle herself and turning into something of an action heroine as she comes face to face with the kidnapper and takes back her child. In point of fact, Olivier's Inspector basically disappears and the "official" investigation into becomes an intensely personal quest for Ann--sort of a psychoanalytic therapy session in action. Bunny Lake is Missing is an interesting and slippery sort of film that always keeps you guessing, shifting allegiances and identification. The casting of Olivier--a gigantic figure in British film--is a stroke of brilliance as Supt. Newhouse is someone the audience instantly feels comfortable trusting. Olivier is charming and calmly paternal throughout, even when he investigatory methods may strike us as odd, indifferent, or even cruel.