As goes New Jersey, so go the Democrats?

Watch New Jersey. It could hold the final key to the 1984 Democratic race. If Walter Mondale carries this state on June 5, the battle could be over. Mr. Mondale will have blunted Gary Hart's strong offensive in the closing weeks of the campaign. Mondale's delegate total will climb close to the required 1,967. Analysts say he will be almost certain to win the party's nomination.

There is, however, another possible scenario. It's one that is keeping this campaign alive, long after the experts thought it would be over. It's a scenario that is making Mondale hurry back to New Jersey again this week, despite his wide lead in the race for delegates.

It goes like this. Mr. Hart ekes out a win in California, where even Mr. Mondale calls the race ''as close as it could possibly be.'' The same day, Hart pulls a stunning upset in New Jersey. Hart would then have won the primaries in the four final major states - Ohio, Indiana, California, and New Jersey. Doubts about Mondale's ''electability'' would mount. The race might then once again be wide open, some analysts suggest.

The hardest part of this equation, however, will be here in the ''turnpike state.'' Even Hart's own campaign team here says he's currently behind. That's why Senator Hart - hoping for a breakthrough - will be here five times in the final three weeks of this campaign.

Is this Hart's kind of state? Hart's own supporters, such as state Democratic Party chairman Jim Maloney, argue that New Jersey voters are similar to those in Connecticut - which went strongly for the Colorado senator.

Mondale backers note that New Jersey lies between New York State and Pennsylvania, which both went solidly for the former vice-president. The truth may lie somewhere in between, and that means the race could be very, very tight.

Millions of Americans, of course, have a rather narrow view of this diverse and prosperous state. It's a picture that is limited to the smokestacks and truck farms lining either side of the 117.4-mile-long New Jersey Turnpike, from the twin spans of the Delaware Memorial Bridge on the south to Newark and New York City on the north.

The ''Pike'' handles an incredible volume of traffic - 143,854,884 cars, trucks, and buses, which carried an estimated 215 million people, last year alone. What those millions of drivers and passengers don't see are the lush, rolling country of northwest New Jersey, the beaches of the eastern shore, the beautiful homes of Lawrenceville, or the Gothic arches of Princeton. ''We took a busload of reporters off the Pike and into the countryside the other day, and they were in awe,'' one Hart worker said with a chuckle.

In fact, this mixture of gritty cities and lush suburbs, smokestacks and ivory towers, old, basic industries and the newest high-tech is what makes New Jersey a fascinating locale for a Hart-Mondale finale. The state gives each man a chance to show off his political muscles.

Throughout this race, Mondale has consistently done better than Hart with certain groups of voters. These include union workers, city dwellers, Roman Catholics, Jews, blacks, older voters, and those with low to middle incomes. Hart gets more the upper-income voters, the young, Protestants, suburbanites, and those in such industries as computers and electronics.

Neither man has done very well at cutting into the other's strengths. With a few minor exceptions, Mondale continues to get the elderly vote, for example, while Hart gets younger voters. For that reason, the same kind of outcome can be expected here in New Jersey, analysts say. And that's one reason this state should be so close. For New Jersey is a amalgam of each man's strengths.

For example, union voters (pro-Mondale) make up 49 percent of New Jersey's Democrats. That is halfway between the union vote in New York (54 percent), where Mondale did so well, and Connecticut (43 percent), where Hart won easily. Jewish voters (pro-Mondale) are 18 percent of the total - again about halfway between New York and Connecticut. Upper-income voters (pro-Hart) are more plentiful in New Jersey than in New York, but not as numerous as in Connecticut. This gives each candidate reason for hope.

Democratic chairman Maloney, interviewed at Hart headquarters in a Somerset shopping center, is helping the candidate find ways to excite the young, well-to-do voters who have supported Hart so strongly this year.

Late last week, Mr. Maloney had Hart tour two toxic-waste sites in northern New Jersey outside New York City. This is just the kind of issue - toxic waste - that troubles young professionals, Maloney says.

New Jersey's largest industry today, Maloney says, is electronics. Many of the young people who have moved here to work in electronics research and manufacturing came from New York. They feel New Jersey is something special, a refuge from urban problems. And they are angered that air and water pollution, toxic wastes, and poor planning could damage the good life they have found here, he says.

''There is a new, different New Jersey out there today,'' he adds.

Hart, trying to capitalize on that change, told a press conference that ''the policies of the past'' - Hart's code words for Mondale - ''will not help the state of New Jersey.'' Those policies, he said, include ''protectionism, energy waste, labor and management confrontation, and environmental damage.''

He continued: ''New Jersey has proved that it is on the cutting edge of change. It has adopted policies (to address) environmental challenges, particularly the toxic-waste dumps.''

What's needed now, Hart said, is leadership in Washington that will act aggressively along with New Jersey citizens to clean up the state's 85 toxic dumps.

Hart's barbs drew a quick response from Mondale.

''Let's take a look at Gary Hart's leadership,'' Mondale said to reporters here. ''(Hart) was on the committee that dealt with the Superfund (the federal fund to clean up toxic wastes). The records show he did not participate for one minute in the hearings. It further shows that he did not participate at all in marking up the bill. And it further shows that he didn't even bother to show up and vote on the measure when it passed. If that's what he means by leadership, then I think the American people will see it for what it is.''

The race here could be so close that the Rev. Jesse Jackson and the black vote could spell the difference. Mr. Jackson could undercut Mondale, and throw this state narrowly to Hart. But if Mondale can hold at least a quarter of the black vote here, he could cling to his current lead.