DON'T LOOK FOR forecasts of national trends in tomorrow's gubernatorial primary in New Jersey. Don't look for hints about the popular reaction to the Reagan tax plan or Dan Rostenkowski or aid to the contras in Nicaragua. Citizens of the nation's ninth-largest state are voting for state offices, notably for governor; and there's not even much suspense about the ultimate outcome in November. Gov. Thomas Kean, a Republican, has conducted himself with aplomb and skill in his four years in office, and is almost universally expected to be reelected. In New Jersey, where the governor appoints all the officers in the executive branch and the county prosecutors besides, that's the big story.

Yet in spite of his lead, Mr. Kean has attracted a number of able Democratic challengers, and in that there is a lesson for the rest of the country. For New Jersey has public financing of gubernatorial elections, and therefore serves as a useful laboratory for other states that don't. Candidates for governor who raise a threshold amount in private contributions qualify for state funds, in return for which they agree not to spend more than $1.1 million on their campaigns. This is the third election in which public financing has been used, and in all but one (Mr. Kean's race this year) there's been serious competition from competent candidates in both parties' primaries. Despite Mr. Kean's strength, the Democrats have a strong field, including Newark Mayor Kenneth Gibson, Essex County Executive Peter Shapiro, senate majority leader John Russo, former U.S. attorney Robert Del Tufo, and former state Sen. Stephen Wiley.

Public financing has served New Jersey well by giving such candidates for the one statewide office that means something the means to reach the voters with arguments and information. That's especially helpful in a state divided between the New York and Philadelphia media markets, with the second-highest TV advertising costs in the nation and relatively little TV coverage of state politics. Unfortunately, the dollar amounts in New Jersey's public financing law have become obsolete over the past decade. Once they purchased a lot of television time. But $1.1 million for an entire campaign doesn't enable candidates to communicate so much in a state where broadcasting a two-minute ad just once on prime time costs $250,000. A law that has promoted competition and communication now threatens to stifle them.

Public financing of campaigns has proved useful in certain specific situations, as in New Jersey's gubernatorial or the nation's presidential races. But its details must be carefully fitted to the circumstances of the contest, and may become obsolete over time. States and localities might be well advised to experiment with public financing schemes. But it's fiendishly difficult to fashion a system of subsidies that fairly promotes competition in 50 different states and 435 congressional districts.