Japanese-American domination of Hawaii's political system is being challenged in a gubernatorial election campaign that has been studded with violence, name-calling and explicit racial overtures.

Both public polls and private assessments show a near dead-heat in voter sentiment between incumbent Gov. George R. Ariyoshi and Honolulu Mayor Frank F. Fasi. They oppose each other in the Oct. 7 Democratic primary, the nation's last, in a state where Democratic nomination usually means election.

The campaign has seen the burning down of a Fasi headquarters on Maui, the beating up of a pro-Fasi poll-watcher and the withdrawal of a third candidate who said his life had been threatened. Each side also has suggested that the other candidate is over-tolerant of organized crime.

Ariyoshi, the only Japanese-American ever to be governor, is regarded even by some supporters as over-cautious, iundecisive and inept. But he now is favored t defeat Fasi, a combative Sicilian-American politician who was severely damaged by a bribery investigation instigated by the Ariyoshi administration.

The probe collapsed when the developer who allegedly gave the bribe said he has lied to the grand jury and refused to be a prosecution witness. The judge dismissed the case without sending it to the jury, but Fasi readily acknowledges that the allegation and the detailed, continuous newspaper coverage left a political "taint."

This view was born out by a Honolulu Advertiser poll in which nearly as many people considered Fasi "extremely dishonest" as considered him "extremely honest." The same poll showed that voters consider Fasi, a 10-year mayor with a reputation for both capable administration and ruthless attacks on political opponents, as considerably more effective than Ariyoshi.

The most significant survey finding was an ethnic one. Ariyoshi had a 3-1 lead among Japanese-Americans and Fasi a nearly 4-1 lead among haoles, as Caucasians are known here. Fasi led by smaller margins among Hawaiians, as only those with some Polynesian ancestry are called, and among Filipinos, Chinese and others in this multiracial state where every ethnic group is a minority.

Japanese-Americans have a well-developed civic tradition, and a consciousness that the ballot box enabled tham to escape the subordinate position they long held here. Consequently, they vote in higher numbers than Caucasians, who hold a slight population edge. The Caucasian numbers include service personnel and dependents, who rarly vote here.

A 1974 survey, when Ariyoshi narrowly defeated Fasi for the gubernatorial nomination, showed that 42.5 percent of the participants in the Democratic primary were Japanese-American, with Caucasians a distant second at 23.1 percent. The figures are considered a likely barometer for the present election.

Both U.S. senators, the attorney general, the leadership of both legislative houses and the president of the University of the Hawaii are Japanese-Americans. Seven out of 10 school principals and most of the teachers in Hawaii also are Japanese-American. So is a majority of the Democrats in the state legislature, which sometimes is referred to as "The Diet" by members of other ethnic groups.

This dominance is producing back-lash among Hawaiians, who hold a disproportionate number or menial jobs, and among Filipinos, who in most cases are more newly arrived immigrants.

Both sides in the campaign have attempted to exploit favorable racial themes white suggesting that the opposition is cultivating bigotry.

Japanese-American voters are told that Fasi is attempting to ride the backlash against them and cause Ariyoshi to be "the first and last Japanese governor of Hawaii." A Fasi leaflet circulating among Filipino voters suggested that Ariyoshi's well-publicized opposition to "a tidal wave of immgration" means he doesn't want to let Filipino workers bring their families to Hawaii.

Ariyoshi's major campaign tool is a slickly produced half-hour television film in which even his parents and the young George Ariyoshi are played by professional actors. This docu-drama features clips from the Japanese bombing of Pearl Harbour and the ensuing evacualtion from their water-front homes of Japanese-Americans, including the Ariyoshi family.

The film, deeply moving to some of the Japanese-Americans who watched it, will be shown repeatedly both on television and at campaign gatherings. It is in part an attempt to remind younger Japanese-Americans. less inclined to vote ethnic loyalties, of the suffering of their parents.

Fasi has his campaign films, too. Probably the best is a series of "time for a change" spots featuring his Japanese-American wife, Joyce.

"We could just dispense with the campaign and hold a film festival," quipped Honolulu Star-Bulletin managing editor John Simons.

That undoubtedly would be fine with Ariyoshi, a 52-year-old lawyer who is seen by his intimates as a thoughtful, private person, and by his critics as a weak executive incapable of speaking effectively or making decisions.

Ariyoshi, who declined to be interviewed, has been as invisible as possible throughout the campaign. After saying he would debate Fasi "anytime, anyplace," he turned down all debate invitations on grounds that his opponent "does not tell the truth." He has rejected most speaking invitations and insisted that a Rotary Club which wanted to hear him submit advance questions in writing. When a television reporter asked why he ahs not investigated the beating of the Fasi poll-watcher, the overor turned away without answering and walked into his office.

Fasi, also in charcter, has been banging away at Ariyoshi with various unsubstantiated charges.

Most of the accusations have derived from a recent Hawaii Crime Commission report, which attributed at least 61 murders in the last 17 years to organized crime. The report painted a chilling picture of syndicated crime activities but was little help in affixing responsibility, since the legislature had refused to grant the commission immunity from libel prosecution.

Fasi, also without naming names, concluded that the report refeered to persons close to the governor because it said that the level of organized crime activity "approaches treason." Ariyoshi replied through his cabinet that the mayor was engaging in "smear and falsehood," and the prevailing view in Hawaii is that the exchange has been damaging to Fasi.

fasi 58-year-old son of a Sicilian immigrant, first came to Hawaii as a Marine in World War II and liked what he saw. He returned after the war with a borrowed $400 and started a salvage business that made him a millionaire.

During his 32 years on the island, Fasi has married twice, fathered 11 children, run unsuccessfully for House, Senate and governor and three times been elected mayor of the city and county of Honolulu, which has a population larger than Boston or San Francisco.

His entire career has been based on fighting "The Establishment," notably Hawaii's tightly organized big businesses and labor unions, the dominant machine in the Democratic Party, and Honolulu's two daily newspapers.

Most of Fasi's political supporters has come from islanders low on the social and economic scale who are attracted to such achievements as cheap city bus service and open air markets and such advocacies as repeal of the sales tax on food and prescription drugs.

But while Frank Fasi is valued in some quarters as a genuine populist who neither forgives enemies nor forgets friends, he is seen by others as an unscrupulous politician who would be dangeroul in highe office.

"Frank is a demagogue who would say or do nearly anything to get ahead," says a prominent Hawaiian businessman who knows both candidates and is voting for Ariyoshi. "And George is so super-cautious that it sometimes seems like he would wrestled sumo too long without a helmet. I don't believe he would ever have anything to do with criminal elements, but I'm not sure he always knows what's going on around him."

In a campaign based so much on negatives, both sides have tried to make virtues of the perceived vices of their candidates. Fasi's brochures advertise his honesty, while Ariyoshi's slogan is "Quiet but Effective."

The Ariyoshi theme was ridiculed recently by Clare Boothe Luce, a 10-year resident of Hawaii and former ambassador and congresswoman. She says she is supporting Fasi because the alternative is "monopoly, one-faction domination" of the islands.

In a passage that was eliminated from the letter she wrote to the Honolulu Advertiser, she contrasted Ariyoshi's campaign build-up with his refusal to expose himself without a script and concluded: "voters are justified in thinking he has been billed as a quiet man because he has a lot to be quiet about."

The Luce complaint captures the essence of Ariyoshi's campaign.His film shows the governor walking unnoticed through a crowded mall while the narrator quotes the Chinese philosopher Lao Tse[WORD ILLEGIBLE]a leader is best when the people hardly know he exists."

By this yardstick of leadership, it is likely that Ariyoshi may have succeeded beyond Lao Tse's wildest expectations. Still, he remains the favorite in an election almost certain to turn on ethnic loyalties and on the seeming reluctance of many Hawaiians to trade what they consider an inept governor for one they do not fully trust.