Sure, a kid could paint that, but did she?

Though its title doesn’t clue you in, “My Kid Could Paint That” is a whodunit of a sort. The question, though, is not who shot the sheriff but who painted a series of pricey canvases?

The artist whose name is on the paintings, Marla Olmstead, was only 4 years old when the fact that her abstract paintings were wowing grown-ups and commanding adult-size prices made her big news. The New York Times did a story, interest rose worldwide (“La Piccolo Pollock,” enthused an Italian magazine) and documentarian Amir Bar-Lev (“Fighter”) knew he had a subject.

Bar-Lev convinced Marla’s parents, Mark and Laura Olmstead -- seemingly nice people who live in Binghamton, N.Y. -- to let him hang out with them, Marla and her brother, Zane. For almost a year, Bar-Lev got access to the family and made this uneven documentary.

Initially, Bar-Lev’s idea was to do a film that touched on the nature of modern art, and some interesting aspects of “My Kid” remain the interview footage with art critic Michael Kimmelman, who notes dryly that many people probably feel “that if a child could do it, it pulls the veil off the con game” of modern art.

Several months into filming, however, something happened that changed everything. “60 Minutes II” did a segment on Marla implying that she was not the sole creator of her paintings but got help from her father, a Sunday painter of sorts. That a hidden camera couldn’t capture Marla completing a canvas was offered as evidence.

Here things get complicated, as reality inevitably does. The Olmsteads offer reasons why Marla doesn’t paint on camera, but they seem to be of different minds about Marla’ success: Mark relishes every moment of it while Laura worries about the effects it will have on the little girl.

Bar-Lev gets drawn more into his film as the Olmsteads see him as their potential defender, but he confides to journalist Elizabeth Cohen, who wrote one of the first pieces on Marla, that he “hasn’t been 100% honest with them about my doubts.”

The longer it goes, the more frustrating it becomes, as Bar Lev declines to come down on one side or the other. It makes his presence in the Olmsteads’ lives serve no real purpose other than exploitation of their misery for his own good. And that is not a pretty picture no matter who paints it.

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“My Kid Could Paint That.” MPAA rating: PG-13 for language. Running time: 1 hour, 23 minutes. In limited release.