The trial of Charles Veverka Jr., a former Dade County policeman charged in the case that sparked the bloody Miami riots, is the story of justice looking for a court free of racial fear.

Call it a trial in search of a city. It already has been moved from three southern cities because of officials' fears it would result in rioting, and at least one black leader in its fourth venue says it could create violence there as well.

Veverka, 29, was granted immunity in exchange for testimony against four colleagues, who were aquitted by an all-white Tampa jury in the beating death of black Miami insurance executive Arthur McDuffie. That verdict spawned three days of rioting in Miami that left 18 dead, 400 injured and $100 million in property damage. In the wake of the riots a federal grand jury in Miami indicted Veverka on charges of violating McDuffie's civil rights, conspiring to falsify police reports and other charges.

The Veverka trial was too hot for Miami, so it was moved to federal court here. But Gov. George Busbee protested that a racially uptight Atlanta could not tolerate the trial -- that the unsolved murders of 11 black children, the disappearance of four others and a mysterious day-care center explosion that killed four had left the city too combustible.

So the trial was moved to New Orleans. There, the defense and prosecution hoped Veverka could get a fair trial.

Then, about two weeks ago, New Orleans police gunned down three blacks suspected of murdering a white officer, and an outraged black community took to the streets in protest. On Monday, New Orleans' white police chief resigned as the city took steps to ease racial tensions. Mayor Ernest Morial phoned the White House to protest the impending Dec. 1 trial and was referred to the Justice Department, which relayed his fears to Justice officials in Miami.

So the trial was on the move again. But to where? Dallas did not have an available courtroom, and defense attorney Dennis Dean objected to Houston, where Miami prosecutor Brian McDonald had won a conviction against white policeman charged with brutality in the drowning death of a Mexican American. U.S. District Court Judge William Hoevler, who will preside wherever the trial is held, rescheduled the trial for Dec. 8 in San Antonio.

The Vererka case has become that of a nomadic tribunal casting about the South for a community whose racial equilibrium will not be disturbed by the sensitive trial.

The police officer turned landscape gardener, Veverka, the father of two, could face 26 years in prison and $26,000 in fines if convicted of the federal charges, which also include playing a role as accessory after the fact to the beating, and filing false criminal charges against McDuffie.

"There's not a city in the South where this trial wouldn't bring some kind of protest," said T. C. Calvert, director of a San Antonio antipoverty program, who expressed concern that the trial has been moved to the quiet Texas city of 800,000 with a majority Mexican-American population and only 10 percent black. "What happened in Miami could happen anywhere, including San Antonio. You have elements here who could create violence if they perceived justice was not done."

The Vererka trial comes as blacks across the country have expressed fear of the random violence against them, exemplified by the slayings of several black men in Buffalo, N.Y., and the Atlanta children. The Klan-Nazi acquittals in Greensboro, N.C., heightened the perceptions of many that equal justice is getting harder to come by in the South.

Such perceptions have been partly responsible for racial violence in Chatanooga, Tenn.; Orlando, Fla., and Idabel, Okla., and have threatened Atlanta, New Orleans and Greensboro.

No wonder a community would choke at the thought of hosting the Veverka case, said Steve Suits, director of the Southern Regional Council in Atlanta, which monitors the region's racial climate. Any city that accepts the trial, he predicted, should witness "an increased division between the black and white community."

"The year 1980 is the worst I've seen for race relations in a decade in the South," said Suits. "There's not a major metropolitan area in the South which doesn't have a severe race relations problem. There's just no good place in the South right now to hold a trial like this."

Judge Hoevler ordered the Veverka case moved to Atlanta after attorneys for both sides interviewed a dozen potential jurors in Miami. Six expressed impartiality; six feared their verdict might touch off more rioting and violence in the community. One black man, a potential juror, pleaded with the judge not to hold the trial in Miami.

In search of a city somewhere in the jurisdiction of the 5th U.S. Circuit Court of Appeals with a pool of jurors unbiased by news accounts of the McDuffie case and subsequent riots, Fbi agents pored over newspaper clippings and reviewed television coverage of the Miami riot in Atlanta, New Orleans, Houston, Dallas and San Antonio. "This move [to San Antonio] uses up about every city on our list," said a Justice Department official.

Early this month New Orleans began to look increasingly unlikely as the site of the trial. In the space of a week:

A white police officer was fatally shote while on patrol.

A grand jury refused to indict two policemen for killing a black man in the mammoth Desire housing project.

Police shot and killed, at close range, a black man who allegedly pulled a knife in the nearby Fisher Homes project.

Officers hunting for killers of their colleague broke into the homes of two black men and a black woman in simultaneous late-night raids near Fisher Homes, and riddled the occupants with bullets. Police said all three shot first.

Blacks were outraged when New Orleans Police Superintendent James Parsons delcared the case of the raids closed. He resigned Monday, amid complaints from black leaders that the suspects were murdered and that 50 plainclothes police in search of the alleged cop killers rounded up dozens of black youths in a housing-project dragnet, intimidating them "Gestapo-style," and beating at least four.

"It was wise to move the trial from New Orleans," said Rose Loving, 54, executive director of a community agency in the 5,000-resident Fisher Homes project. "The trial, and a verdict perceived by the community to have been wrong, could have upset everything we've done to try to keep things cool here.

"I would have feared violence, of something erupting, with people letting their frustrations go. The projects have been pent up since all this has been going on. That [the Veverka trial] might have been the breaking point."

Defense attorney Dean says it may be impossible to locate a community with a bias-free jury pool. "Most people perceive the McDiffie trial as white police brutalizing blacks," he said. "When people hear 'McDuffie,' that's what they think. Veverka is not charged with that."

But if any community can handle the Veverka trial, it is San Antonio, according to Bernardo Euresta, a city councilman. "We've only had a few protest marches and some picket lines, even back in the '60s," he said. "We can handle the trial."

But Calvert of the antipoverty program is not so sure. "It could create violence here if justice is not done," he said.

Meanwhile, some Miamians think the trial should be returned there. "We need to air our own dirty linen right here in town," said Garth Reeves Jr., publisher of the Miami Times, a 24,000-circulation black weekly. "It's unfair to try to palm it off on some other city . . . .

"No community wants this trial because there isn't a city in America with enough guts to send a white law enforcement officer to jail for killing a black person. This case is backed by enough hard evidence to send him to jail. Justice won't be done unless Veverka is convicted."