A referendum is planned here Tuesday amid the steamy dog days of August, yet hardly anyone knows about it, least of all the voters.

They are missing a good show that could mark an important milestone in the political realignment of Miami, once a bastion of Democratic liberalism.

Technically, a simple charter question is involved: Should Miami switch from its weak mayor/city manager form of government to the strong mayoral system of most major American cities?

But the issue has become so entangled in the city's Byzantine ethnic and personality politics that voters would have little difficulty concluding that the referendum really deals with who should run the city -- Republicans or Democrats, Ronald Reagan or Walter F. Mondale, Cubans, blacks or The Miami Herald.

Debate has been conducted in the gutter. For example, the Tiger Bay Political Club, the state's premier forum for 22 years, invited the city's mayoral candidates to visit recently and four of six appeared.

One said "right-wing fascists" were trying to take over the city with "a wave of McCarthyism." Two argued about whether a grand jury should subpoena one or the other. The fourth told an opponent, "I hope you are more successful in your law career than you've been as a candidate."

Most observers agreed that the clash was mild by Miami standards. "It's not playing rough; it's playing crazy," groaned J.L Plummer, a mortician and 16-year city commission member.

The five-member city panel has inspired guffaws here, being one of few local government bodies in the world with its own foreign policy, among other idiosyncrasies. It favors right-wing Nicaraguan counterrevolutionaries and opposes South African apartheid and is on record against Prince, the pop recording and movie star, for singing "unholy" songs.

Miami has undergone an identity crisis. As mayoral candidate Marvin Dunn notes: "One day, 'Miami Vice' [the popular television crime show] gets 15 Emmy nominations, and we think we're great. The next day, we're declared the murder capital . . . . It's a roller-coaster mentality . . . . But underneath it all is a basic feeling of self-doubt."

In the last decade, Miami has become a major banking and trade center and a truly international city -- "the capital of Latin America," some have said. But it has also become the nation's murder and illegal drug capital, and its economy is in the doldrums.

The area has dropped to fifth among Florida's most popular tourist spots, 6 million square feet of office space stand vacant and a host of high-technology firms have chosen to locate elsewhere in the state. Television viewers and newspaper readers are fed a steady diet of murder, mayhem and drug busts.

Ironically, Mayor Maurice Ferre and many others say they think that "Miami Vice" has given the city a shot in the arm.

Deep racial and ethnic divisions have created rapid political changes in Miami and surrounding Dade County, normally heavily Democratic.

As recently as 1980, 73 percent of county voters registered as Democrats and 19.6 percent as Republicans. Today, 59 percent register as Democrats, 33.5 percent as Republicans. The overwhelming majority of the city's blacks is Democratic; the overwhelming majority of its growing Hispanic population, mainly Cuban-Americans, is Republican.

City commissioner Joe Carollo, a Republican Cuban-American, is chief exponent of a strong mayor form of government and supports a companion measure on Tuesday's ballot that would make the mayor's office partisan. He argues that Miami has a "newspaper form of government," dominated by The Miami Herald, which he says is viewed as "the Sunshine Pravda" in the Cuban community.

The November mayoral election, which now pits candidates of all parties, plays a key role in divisions over the issue. If the charter changes pass Tuesday, Carollo is expected to enter the race and would be the best-known Republican in a crowded field.

Chief opponent of the changes is Cuban-American Raul Masvidal, a banker and registered independent whose candidacy would be damaged by charter changes. "We don't need more ways to divide this city; we need ways to unite it," says Masvidal, considered the candidate of the business establishment.

Dunn, the only black in the race, says he would become the Democratic nominee if the partisan-election measure passes, because 55 percent of registered Democrats are black. But he opposes it as "a personal grab for power" that would "plunge this community into conflict."

Democrat Ferre, mayor for 12 years, opposes the partisan-mayor measure and supports the strong-mayor concept. He is suspect of the way Jeb Bush, Dade County Republican chairman and son of Vice President Bush, has adopted the issue, expressing concern that it may help elect a Republican mayor.

"City Hall is important to the Republican Party and George Bush," Ferre says. "It would consolidate the inroads the party has made in registration. It would put them in a position to mount an assault on longtime Democratic Rep. Claude Pepper and help Republican Sen. Paula Hawkins in her 1986 race."

Jeb Bush, who moved to Miami after the 1980 election, says the election offers the GOP "nothing in the short run" but adds that "we'd have a very good chance" of electing a Republican mayor in two years