The “Everybody’s Talkin’ ” singer and John Lennon’s self-described favorite “group” gets the full-on rock-doc treatment normally accorded to household gods like the Doors and Lennon himself. John Scheinfeld’s film traces a familiar trajectory, moving from its subject’s humble beginnings through commercial and artistic success to that inevitable rock-star decline of drugging, boozing, and bankruptcy. But as interviewees like Brian Wilson, Robin Williams, and Yoko Ono insist, Harry Nilsson did everything a little differently—refusing to cement his fame by subjecting himself to the rigors of touring and, later, galvanized by Lennon’s death, shelving his musical career in favor of gun-control activism. If Scheinfeld doesn’t share his subject’s iconoclastic taste, sticking closely to the archival footage and talking-heads formula, it’s the quality of the former (such as Nilsson’s oral autobiography) and the sense of personal involvement in the latter that elevates the film above the run-of-the-mill rockumentary. The director doesn’t bother to interview the experts—only those who knew the man best—a strategy that yields such anguished moments as Nilsson’s first son tearfully recalling his one-night reunion with the father who had abandoned him years earlier.