The California Supreme Court narrowly approved today a Democratic Party reapportionment plan, leaving the state's Republicans with only a slim chance of overturning the scheme, which might cost the GOP five congressional seats.

The 4-to-3 decision written by Chief Justice Rose Bird, who was appointed by Democratic Gov. Edmund G. Brown Jr., said the plan drawn up by Democratic Rep. Phillip Burton and passed by the Democratic-controlled legislature last year was "the least disruptive" way to conduct this year's election.

The decision allows a Republican referendum to remain on the June primary ballot. That referendum would, if passed, require the legislature to reapportion again for the 1984 elections. But the court's approval of the Burton plan for this year's general election makes it likely the legislature would remain in Democratic hands and thus unwilling in 1984 to change district lines to save the Republicans.

"It's the typical political mashed potatoes," said freshman Republican Rep. David Dreier, who has been forced into the same district with another Republican incumbent under the Burton plan.

Dreier called the redistricting plan an effort "to upset the voters' mandate" and said the only hope was for voters to pass another Republican initiative on the ballot this year that would turn over the new reapportionment duties to an independent commission. Many other politicians, however, expect such a commission would become just as politicized as the legislature because its members would be appointed by members of the rival parties.

State Senate President pro tem David Roberti, a Democrat, praised the court's "fair, dispassionate decision, recognizing the fact that our plans conformed to one man, one vote." Senate Republican leader William Campbell, however, called the decision "an unbelievable example of judicial arrogance and judicial tyranny" and other Republicans said an effort would be made to get the federal courts to overturn the ruling.

The California congressional delegation, now composed of 22 Democrats and 21 Republicans, gains two new seats in 1982 because of the state's population increase. Republicans charge that the Democrats have aborted what would have been an increase in the number of Republican congressmen resulting from population gains in suburban, usually Republican areas.

Burton, who referred to his plan as "gorgeous, it curves in and out like a snake," grabbed chunks of Democratic voters from all over the San Francisco Bay area to bolster the seat of his brother, Rep. John Burton. He destroyed the political base of one adversary, Republican Rep. Robert K. Dornan and threw another adversary Republican Rep. John Rousselot into the same district with Republican incumbent Carlos J. Moorhead.