Robert Oliver, age 7, is a problem child. He has killed several cats and dogs, his grandmother says, and has attempted suicide. As a result he is on Ritalin for attention-deficit disorder and BuSpar for depression.

Rory Kennedy and her cinematographer, Nick Doob, have come to Eupora, Miss., a tiny town with a median household income under $25,000 a year, to follow Robert's progress. Their intention is to make a film about how social services programs affect the lives of American children living in poverty. But the resulting gripping documentary, ''A Boy's Life,'' on HBO tonight, turns out to be about a wicked witch.

Ms. Kennedy, who dealt with Southern poverty in her first film, ''American Hollow,'' about an extended family in Appalachia, is becoming quite a filmmaker. It is difficult to take your eyes off her subjects or their plight. It still seems important to mention that Ms. Kennedy is the youngest child of Robert F. Kennedy, and that she was born in 1968, six months after his death, but her professional reputation is growing and that fact may soon be considered incidental.

''A Boy's Life'' first visits Robert at home, where he pounds on the floor and bangs his head against the wall. When someone mentions that his little dog is adorable, he replies, ''But sometimes he can be a little devil and bite you with his sharp teeth.'' Robert does seem hyperactive, practically bouncing off the walls, despite the Ritalin.

Then the film follows Robert to school. He sings ''My Country 'Tis of Thee'' along with his classmates, he reads more than competently, he says ''Yes, ma'am'' to his teachers, and -- can this be? -- he makes the honor roll.

''I think what we've got here is two Roberts,'' his principal, Vicky Beckham, tells Anna Threadgill, Robert's grandmother, during a home visit. Anna is not pleased by the suggestion that her grandson's teachers can control him but she cannot, and she reacts with a veiled version of her deadly modus operandi.

When Ms. Beckham assures Robert that he has everything he needs for success, and specifically that he is intelligent and nice-looking, Anna responds immediately, taking on her grandson's voice: '' 'I'm good-looking, and all the kids are jealous of me, and they all call me ugly,' '' she says. ''But say, 'I know I'm good-looking.' ''

If this is Anna's good behavior for the camera, one shudders to imagine how she treats Robert when Ms. Kennedy and Mr. Doob leave. And you don't have to have grown up on welfare to recognize and be outraged by the pain that an emotionally abusive parent or guardian can inflict. Poverty and a culture that discourages hope only magnify young victims' helplessness.

When Anna mentions that her father was a full-blooded Comanche, Robert goes into his tough-guy act, saying: ''Give me a bow and arrow. I need to shoot myself.'' His grandmother responds by handing him a pistol (unloaded at least) and then ridiculing him. ''You can't even shoot Mamaw's gun,'' she says.

Robert and his little brother, Benji, sleep in the same bed with Anna, although the house seems to have enough space for other arrangements. When Robert wins a race with Benji, she declares Benji the winner instead and says, ''Robert, you don't know how to run.''

By the end of the film you have to cringe whenever Anna touches Robert. He cringes, too, thank goodness.

Robert's mother, Robanna Fason, was 15 when she became pregnant as a result of rape. She was running with a ''bad crowd,'' she says. ''They got me on drugs and some kind of something that made me where I didn't know what my name was.''

Robanna doesn't take care of her children, she says, because she is sick. ''I'll stand in the store for five minutes, and my legs go to hurting,'' she says by way of example of her condition, also mentioning pneumonia, seizures and thyroid problems. When she seeks medical attention, though, Anna ridicules and discourages it.

Anna has problems herself. Dr. Virginia Fee, Robert's state-appointed therapist, concludes that Anna has something like Munchausen syndrome by proxy, inducing symptoms of emotional illness in Robert. The film suggests that Anna despises him because his arrival destroyed Anna's dreams for her daughter. She had planned for Robanna to be a beauty queen and a model, even though Robanna, in her early 20's, is obese and missing several front teeth.

During the film the best thing that happens to Robert is that Anna goes into the hospital, and that leads to some changes. It is unclear exactly how ill she is or how much her mind is influencing her body, but when on her sickbed Anna promises Robert that she will see him again in heaven, it sounds like a threat.

A BOY'S LIFE

HBO, tonight at 7:30, Eastern and Pacific times; 6:30, Central time

Produced and directed by Rory Kennedy; Liz Garbus, producer; Nick Doob, co-director and director of photography; Charlton McMillan, editor; Joel Goodman, original music; Mark Bailey, story editor; Nancy Abraham, supervising producer for HBO; Sheila Nevins, executive producer for HBO. A Moxie Firecracker Films production.

Photo: Anna Threadgill and Robert Oliver in ''A Boy's Life,'' on HBO tonight. (Photo by HBO)