When actor Michael Rapaport set out to make his directorial debut, he picked a documentary subject long dear to his heart, gained intimate access to all of his subjects and captured more than 200 hours of raw footage. So far, so good. But the real drama kicked in after the film was finished.

“Beats, Rhymes & Life: The Travels of a Tribe Called Quest,” his account of the storied alternative hip-hop group, premiered in competition at Sundance last week, and there were some very notable absences from the Temple Theater — namely, three-fourths of the group.

Back on Dec. 2, the day after the film was first announced as a Sundance selection, A Tribe Called Quest’s founder and most visible member Q-Tip took to Twitter, saying, “I am not in support of the A Tribe Called Quest documentary … the filmmaker should respect the band enough to honor our request regarding the film,” without going into further detail. A few weeks later, he added: “We will never be taken advantage of like we were in the past. We don’t care who it is.”

Q-Tip, along with bandmates Ali Shaheed Mohammed and Jarobi, later released a tersely worded statement offering support on the eve of the festival, but has been silent since. Fellow founding member Phife Dawg was present at the screening with his wife, and even broke down in tears during a subsequent Q&A.

Rapaport, interviewed while watching the NFL conference championships the day after the premiere, himself still is unsure exactly where things got complicated. “I wasn’t hired by the group to make this movie,” he says. “We had a legal agreement from the inception — they don’t have final cut, and everything was above board, everything was signed off. I’m not really sure what happened.

“I can’t really speak for (Q-Tip) and what he was thinking. I do know that when I talk to him face-to-face, he’s been really excited about the film. So the other Internet stuff was a little strange for me.”

A possibility is that the film may have turned out more revealing than anticipated, as Rapaport was witness to some intense contretemps between Q-Tip and Phife offstage during a stint at 2008’s Rock the Bells fest, which led to a prolonged, though not then public, falling-out.

“I got a lot more information than I bargained for,” Rapaport says. “I had no idea it was going to unravel the way it did. But the unexpected is the beauty of documentary.”

It’s unclear whether the behind-the-scenes drama will have an adverse affect on the film’s fortunes, or precisely the opposite. The last time a documaker unwittingly captured a band on the verge of falling apart — Metallica docu “Some Kind of Monster” — the band came out in complete support of the pic, doing the full press circuit and even chipping in their own money just to keep the film afloat.

Here, the group in question is credited as a producer on the film, though Rapaport notes “they had no involvement as producers” aside from providing music clearance and offering support. Having the group on hand to promote it certainly would be helpful, however the controversy has attracted its share of attention as well.

Which is ironic, as Rapaport never set out to make an expose. A fan of the group since before it was even active, — he recalls hearing Q-Tip’s first guest verse on the Jungle Brothers’ “The Promo” back in 1988 — the director initially paid for the movie out of his own pocket before picking up investors along the way.

“From the beginning, I just knew they were special,” he says. “I don’t think Tribe ever made a bad song.”