To Sen. Edward M. Kennedy, the June 3 California primary is the last hope and best chance of staying in the presidential race until the Democratic National Convention.

To the supporters of President Carter, the primary is an opportunity for conclusively ending the Kennedy challenge while demonstrating that Carter can win in a pivotal state he lost in the primary and general election four years ago.

But to many California Democrats, according to the latest findings of veteran California pollster Mervin Field, the contest is among two declining candidates and a "none-of-the-above" choice, which is steadily gaining on the leaders.

Field's latest poll, which will be published Friday in California newspapers, shows Carter and Kennedy in a dead heat with 33 percent each. Gov. Edmund G. (Jerry) Brown Jr., whose name remains on the ballot although he is no longer a candidate, has 7 percent. This is a decrease for all three candidates from Filed's April poll, when Kennedy led Carter 42 to 39 percent.

The only gainer in the past month has been the category of "undecided-other candidates," up from 10 percent to 27 percent. Voters have an option of a new ballot category marked "unpledged delegation." If enough voters make this choice, it could trigger a free-for-all in Democratic congressional district caucuses that will be held after the primary.

Field believes most Democrats nonetheless will wind up voting for either Carter or Kennedy.

"But such a victory would not appear at this time to be based on any strong enthusiasm for the winner," Field said today. "Many voters who support Kennedy or Carter don't think that the candidate of their choice will do a satisfactory job. This could be a ripe state for [independent candidate] John Anderson."

It also could be ripe for Republican Ronald Reagan, who leads George Bush 72 to 11 percent in today's Field poll, virtually the same margin he held a month ago. Bush has canceled the remainder of his California campaign schedule as he contemplates dropping out of the race.

However unenthusiastic the Democratic voters may be, supporters of both Carter and Kennedy still believe that a lot of prestige is at stake in California, in addition to the 306 national convention delegates that will be chosen.

Because of California's primary voting tradition and the usual presence of several controversial ballot measures, the voter turnout here is expected to be more than twice that of any other state. In 1976, Californians cast one of every 5 1/2 primary votes in the nation, and the total turnout on June 3 is expected to be about 6 million. t

Democratic National Finance Chairman Charles T. Manatt, one of the leaders of the Carter campaign in California, predicts that the president will win the primary. But other Carter backers are less optimistic.

State Treasurer Jesse M. Unruh, a Carter backer who is widely regarded as one of the state's shrewdest politicians, says that the race is close and that Carter could probably clinch it by making a pre-election visit. Such a visit reportedly is under consideration.

Los Angeles attorney Nelson Rising, a leader of the Kennedy campaign, doesn't think a presidential visit would make any difference.

"Based on the experience of the past, the more visibility Carter gets, the worse he does," Rising said. "The Rose Garden strategy recognizes that."

Whatever Carter decides, the Massachusetts senator is campaigning hard in California at a variety of events, some of them imaginative. Kennedy's Saturday schedule, for instance, includes a rally in the Mexican-American community of East Los Angeles, a fund-raiser with the city's gay committee and a 20-course dinner with Taiwanese-Americans.

But the chief reliance of the Kennedy forces is on a new advertising campaign that will be launched this weekend on the theme of, "If you want a choice at the convention, there's only one choice in the California primary."

Meanwhile, the Carter side is relying on its usual surrogates -- Vice President Mondale last week and First Lady Rosalynn Carter today. Carter has the support of most California mayors, but the true feelings of some of them may have been expressed by San Francisco Mayor Dianne Feinstein last week, when she told a Mondale audience that most California Democrats look forward to the end of the primary campaign.

If the race is as close as it is expected to be, the votes cast for Brown could provide the margin of difference. Brown, whose favorability has slumped to 33 percent in the latest Los Angeles Times poll, is not endorsing any candidate, and his chief aide, Gray Davis, says the governor is "putting presidential politics behind him and concentrating on state issues."