It doesn't have a British accent, it isn't even remotely quaint, and an oil company didn't pay for it, but it is on public TV. "Non-Fiction Television," a series of ambitious, independently produced American documentaries, begins its second PBS season tonight at 10 on Channel 26.

The first program is almost literally a killer: "Deadly Force," Richard Cohen's gripping and persuasive investigation of the fatal shooting of an unarmed man by a Los Angeles policeman in 1977. Although it deals with the specifics of this incident, the one-hour tape is really a troubling, thoughtful inquiry into the wider subject of police brutality and the whole relationship between society and its custodians of order.

Documentaries shown in the "Non-Fication Television" series are not like those produced by commercial network news departments. They usually have a distinct point of view, they do not aspire to showing every single side of every single issue, and they are not offered up as great gollywhompers of conglomerated information.

In its first season, the programs funded (paritally or entirely) and shown on the air by the project ranged from the opening bombshell, "Paul Jacobs and the Nuclear Gang" -- broadcast, probhetically enough, just three weeks before the Three Mile Island story broke -- to the hip, impish humanism of "La La, Making It in L.A.," about hungry hopefuls hobnobbing in Hollywood.

Unfortunately the lack of quanintness, British accents and oil money doomed "Non Fiction" to low priority at PBS. The shows were scheduled at erratic hours and given little promotional support. PBS is awfully busy processing money into red tape and cannot always be bothered with Real TV.

This year, however -- probably after considerable lobbying by project director David R. Loxton and coordinating producer Katherine Kline at New York's Channel 13 -- "Non-Fiction" does have been given a regular Friday night spot in the lineup, at least for the next 13 weeks.

Amoung the programs to be seen this season are "America Lost and Found," a timely look at how the American psyche was jolted by the Great Depression; "No Maps on My Taps," a long-delayed portrait of three black jazz tap dancers and their heritage; and, perhaps the most potent item on the agenda, "One Company Business," a three-part, three-hour report on the CIA.

"Deadly force" gets the series off to a strong, commanding start. If focuses primarily on the case of Ron Burkholder, shot six times and killed by an L.A. police sergeant in 1977 even though Burkolder, at the time of the shooting, was not only unarmed but totally naked.

Exactly why he was naked while standing outdoors at a pay telephone is never made clear, but filmaker Cohen painstakingly reconstructs the incident and its aftermath through interviews with friends and relatives of the victim and news footage of an inquest into the killing. At the inquest, the sergeant who fired the shots refused, under his fifth Amendment rights, to answer any relevant questions. No criminal charges were ever brought against him.

Cohen wanted to tell the story as visually and naturally as possible, with no narration and little superimposed information gingerbread. Sometimes this is confusing, but more often it draws one into the story.

Details about Burkholder's background are left hazy, perhaps because Cohen is interested in him more as a symbol than as a victim. His commonlaw wife talks about how affable he was, but the official version of the incident has him coming at the officer in a threatening way and grabbing the officer's billyclub away with "maniacal" and bionic strength which, it is alleged, may have been induced by some drug Burkholder may have taken.

This is a case filled with its and mysteries on both sides.

There is more to the documentary than inquisition and accusation. The program is cleverly edited to put components of the legal system into sometimes absurdist perspective -- from demonstrators ritually chanting "Jail the killer cops" to an attorney demonstrating the trajectory of bullets on what looks like a Gay Bob Doll.

How "fair" is the documentary to the Police? Its viewpoint is clear enough: that in the pursuit of order, the law may suffer, that those with the power and guns of enforcement may not be answerable enough for their judgement calls. But it is not an indictment of any police department nor a protracted political whine.

Police officials and others defending the force, and the use of deadly force in the Burkholder case, actually do a fairly good job of indicting themselves. Ed Davis, former L. A. police chief ("slightly to the right of Darth Vader,"' as Johnny Carson might say), comes off an arrogant buffoon in a piece of videotape he made to be shown to L. A. police officers after one of them, wearing a mask, admitted to a TV reporter that the use of force by cops is sometimes almost a sport.

Other scenes invovling the district attorney and the lawyer who defended the policeman look discomfortingly like chilling, real-life replicas of episodes from the political thriller "Z". These men appear far more obsessed with the interests of the bureau than with any vague ideal of justice. o

After eight months of delay in investigating the shooting, and the final, official exoneration of the sergeant, we see a new police chief ushered in to the tune of Gov. Jerry Brown's praise for a police department "whose traditions are excellent and whose reputation is beyond question."

Burkholder's mother was interviewed by Cohen, not for teary effect but for a lucid and dispassionate account of the issues involved in her son's death and the protesting it took to get it investigated: "I feel it's important to uncover the way people are treated . . . by the authorities," she says. "I think we are really due a little more rspect . . . Why don't they use a little more thought before they shoot?"

"Deadly Force" is a stirring argument on behalf of a little more thought, and with other documentaries in the "Non-Fiction" series, it could bring a lot more thought to public television in the weeks ahead.