In California, Prop 13 legacy means no icing on cake . . .

California, the nation's richest state, is like a wealthy gentleman whose stocks have been slipping in the market: He's still quite well off, but he may have to forgo - at least for a time - some of the amenities to which he has become accustomed.

There are those - especially some city and county officials - who are more inclined to compare the state to a properous citizen who has been suddenly beggared. Cutting back police and fire departments, letting streets go unrepaired, and eliminating school programs, in their view, amounts to more than losing ''amenities.''

The situation is partly Californians' own making and partly due to the national economic slump and federal budget cuts.

Gov. Edmund G. Brown Jr., signing a fragile $25.2 billion state budget June 30, just hours before the beginning of the new fiscal year, remarked that for the first time since 1943 the new budget was lower than the preceding one.

Had the Legislature been willing to vote some new taxes, the full $27 billion spending program proposed by Governor Brown might have been approved. Before the June 8 state primary, the governor had suggested an oil severance tax, and the speaker of the state Assembly, Democrat Willie Brown of San Francisco, mentioned higher levies on candy, cigarettes, and liquor.

But after the voters overwhelmingly approved a proposal to make permanent a temporary indexing plan for income taxes and another to repeal gift and inheritance taxes, not many legislators were inclined to vote for new taxes.

The electorate that cut local property tax collections in half by approving Proposition 13 in 1978 remains in a tax-cutting mood. In numerous local elections as well as in the June 8 state vote, Californians have made clear that they feel taxes are still too high. No matter that many city, county, and school officials insist there is no longer any ''fat'' to cut and that communities will eventually pay a steep price for shortsighted economies.

Like many other states, California has a law requiring a balanced budget. The million out of balance by February. By trimming some programs and speeding up some revenue collections, the governor and Legislature managed to bring it into theoretical balance.

There was even some hope that there might be a $235 million surplus when the budget year ended at midnight June 30. The Republican minority in the Assembly, led by Robert Naylor of Menlo Park, held up agreement on the budget for some time by first insisting that there be no new taxes and then trying to earmark the apparent surplus for aid to local school districts. That won on the first point but lost on the second - fortunately, as it turned out.

On the morning of July 1 state controller Ken Cory, the man who pays the state's bills and has to tally the final balance between revenues and expenditures, called a press conference to announce that only by postponing several million in payments was he able to tentatively close the books on fiscal 1982 with $33 million left in the till. Final figures will not be known until September, and Assemblyman Naylor says he feels there is likely to be some $230 million on the plus side at that point.

Mr. Cory says that ''unless Reaganomics begins to work soon,'' state revenues from sales, income, and other taxes will continue to lag behind the inflation rate. If so, the controller asserts, ''local aid may have to suffer more cuts.''

A different view comes from state legislative analyst William Hamm, whose economic projections have a great deal of influence on spending programs devised by the Senate and Assembly. Schools and local governments ''still are getting lots of aid,'' he declares, ''and the property tax still is a good revenue producer.'' Revenues from that source continue to rise despite Proposition 13's limitations and the effects of recession, he points out.