“Keane” opens in the chaos of the Port Authority Bus Terminal, as a man searches frantically for his abducted 6-year-old daughter. But what seems at first to be a sentimental child-loss drama soon gives way to an opaque character study of a man on the verge of mental collapse.

William Keane (Damian Lewis) talks to himself, attacks strangers, and creates unsettling situations while trying to get by on his disability benefits in the outskirts of Midtown. As he willingly hurts himself and others with shocking indifference, the goodwill we feel toward him in the first few minutes is quickly wasted.

Refusing the comfort of a soundtrack, this spare film follows Keane’s every movement – director Lodge Kerrigan fills nearly every shot with a close-up of Mr. Lewis’s disturbed face. It soon becomes clear that his mental instability may have little to do with the loss of an actual daughter. But the film does not provide much other insight into this man’s inner life.

Some uncertainties – like whether his daughter was abducted, or even existed – are provoking, but most annoy. Keane’s mental instability seems to wax and wane as is convenient for the narrative. He seems crazy when it makes for a compellingly awkward scene, and mentally competent when he wants something – like companionship or anonymous sex.

Keane’s inexplicable mental issues leave the audience with strong feelings of anxiety, but the people onscreen seem oblivious to his darker side – as when Lynn Bedik (Amy Ryan) entrusts this unsettled man from her motel with her young daughter, Kira (Abigail Breslin). Despite the odd circumstances of their encounter, the scenes between Mr. Lewis and the charmingly fragile Kira, winningly played by Ms. Breslin, bring a captivating humanity to the film.

Mr. Lewis provides a strong presence throughout this mental unraveling, but with Kira, the incongruities of his character begin to find a purpose. Keane’s tenderness with her is reassuring – until it becomes clear that he is not equipped to protect her from the dangers of others, or himself.

From the tawdry motel where Keane and the Bediks stay to the bars and diners they frequent, Mr. Kerrigan seems focused on perpetuating an aura of anxious instability. This is a side of New York City that most residents try their best to avoid.

By the end, the complete discomfort that Mr. Kerrigan has created seems like a forced experiment – one that may have been a rewarding challenge to create, but is difficult to watch, closer to asphyxiation than entertainment.