A six-month study by the Institute for Southern Studies has concluded that Ku Klux Klan and Nazi gunmen who were accused of killing five members of the Communist Workers Party at a Greensboro, N.C., street demonstration Nov. 3, 1979, had an "intimate alliance" with the local district attorney and police officials who later handled the case.

Six of the Klansmen and Nazis were charged in connection with the deaths, but were acquitted last November.

The institute, a private non-profit organization that monitors reports of civil liberties violations, also charged local prosecutors and the district attorney's office with "systematically weakening the prosecution" of those accused of the murders and of allowing persons on the jury who believed "it's less of a crime to kill communists."

The Reagan administration was criticized for not prosecuting the Klan members on charges of violating the civil rights of the slain demonstrators.

The outgoing U.S. attorney for that section of North Carolina, H. M. Michaux, recommended prosecution to his successors before he left office earlier this year.

Georgia state Sen. Julian Bond, president of the institute, based in Durham, N.C., said yesterday, "Federal inaction in this case reveals the complicity of the Reagan administration in fostering a new permissiveness toward racial separation, racial inequality, racial isolation that eats away at our national unity."

"We have come to Washington today because the intimate alliance between public officials and terrorists in Greensboro demands vigorous federal scrutiny and prosecution," he said.

Comparing the civil rights efforts of the Justice Department during the first six months of the Reagan administration with those of other administrations, Bond said, "I would rate Carter pretty good, Nixon fair and Reagan miserable."

William Bradford Reynolds, head of the Justice Department's Civil Rights Division, said his division "has been investigating the question of whether federal criminal charges can be brought against anyone for the Greensboro, N.C., shootings.

"We advised the city April 29, 1980, that our investigation provided no basis for criminal prosecution of any member of the Greensboro Police Department in connection with the incident," he said. "We have never investigated the prosecution of this case by the district attorney and plan no such investigation because we know of no basis for such an investigation."

He said the Civil Rights Division will examine the institute's report.

The study accused Greensboro police of "gross negligence" in failing to prevent the deaths of the five demonstrators.

It said the police department's "failure to be on the scene to prevent violence amounts to gross negligence and raises grave questions about their motives for such inaction."

Evidence was cited that police cars drove past the Klan-Nazi rendezvous point where shotguns and rifles were visible and that police "watched and photographed" the formation of the nine-vehicle caravan of Klansmen and Nazis.

In addition, police units normally assigned to the area of the rally had been instructed to leave shortly before the shooting began.

A spokesman for the Greensboro police, Hewitt Lovelace, said he had not read the report, but he said its charges about the police were "ludicrous."