“Billie” has one of the most unusual and (at least in its initial presentation) disturbing hooks for a documentary in some time. It begins by talking not of Billie Holiday but of Linda Lipnack Kuehl, an arts journalist who in 1971 embarked on a biography of the singer Holiday. That work was never completed; Kuehl died in 1978, in what officials deemed a suicide.

Kuehl amassed a formidable research archive, including tape recordings of interviews with Holiday’s collaborators, friends and lovers. (These categories frequently overlapped.) Some of her work was used in subsequent published biographies, but this movie’s director, James Erskine, acquired the rights to her entire collection, and “Billie” is the first project he derived from it.

Holiday’s short life — she died in 1959 at the age of 44 from complications related to substance abuse — was packed with incident, much of it upsetting. She was on the receiving end of awful racism (as a Black female singer for a couple of white bandleaders in the 1930s, she couldn’t stay in Jim Crow-era hotels or even use their washrooms) and fell prey to multiple addictions. But she also lived her high life with a level of proud ostentation.