The goverment index designed to predict behavior of the economy plunged 3.3 percent in April, its steepest drop ever, the goverment reported yesterday.

Although the drop was exaggerated by special factors, the decline bolstered other recent signs that the economy is slowing. The government also reported that new factory orders, another key indicator, fell 6.1 percent in April.

The statistics were the latest in a series of gloomy figures that show the economy clearly is slowing from its rapid pace of late 1978 and early 1979 and may be entering what is expected to be mild recession.

Meanwhile, the Agriculture Department predicted that because of higher-than-expected increases in marketing and processing costs, retail food prices probably will rise more rapidly this year than the 10 percent it forecast earlier.

The department reported yesterday that farm prices rose by three-quarters of a percent in May, slightly less than in previous months. Farm prices last week were 14 percent above their level of a year ago.

And the Labor Department reported that wages and salaries rose an average 2 percent across the nation during the first three months of this year - up from a 1.5 percent rise in the final quarter of 1978.

The department also announced that new hiring by employers dropped by 0.3 of a percentage point in April, the largest monthly decline since the start of the 1974 recession.

The series of statistics heightened the debate about whether the economy is heading into a recession. The Carter administration's official view still is that the nation will avert a true recession. A recession is two consecutive quarters of decline in the economy.

Treasury Secretary W. Michael Blumenthal yesterday trimmed his estimate of the economy's likely growth rate this year to between 1.5 and 2 percent - from a 1.7-to-2.3 percent forecast previously - but discounted any slump.

However, economists outside the government appear to be more convinced than ever that a recession is on the horizon, with some even contending that the downturn already has begun.

George L. Perry, a Brookings Institution economist, said in an interview he believes "there's" a good chance that the recession already has started," and that the downturn may be somewhat deeper than had been expected.

And Murray L. Weidenbaum, a Republican economist, predicts a recession beginning in early summer and possibly lasting through the first quarter of next year. Weidenbaum says inflation will slow only moderately.

The new fears of imminent recession are in sharp contrast to the mood only a few weeks ago, when some analysts - both in and out of government - were afraid that the economy might be overheating.

The Carter administration underwent an internal battle over that issue, with several top advisers openly campaigning for the Federal Reserve Board to raise interest rates, and eventually being overruled by Carter.

Even now, economists say they still are unsure just how much the economy is slowing. Although recent figures have been bearish, many have been depressed by the impact of the Teamsters' strike. The situation still is clouded.

The April decline in the index of leading indicators was the largest on record. The only drop approaching it was a 3 percent dip at the start of the 1974-75 recession. The slump then was the worst in 36 years.

However, the Commerce Department noted that the decline stemmed largely from a drop in the length of the average work week, which itself was distorted by the impact of the Teamsters' strike and the Easter and Passover holidays.

The department estimated that without that dip in the work week, the index would have fallen 1.6 percent. A perliminary estimate that the index fell in March by 0.5 percent was revised to show an 0.3 percent rise.

However, the index declined slightly in both January and February. Some economists say, as a general rule, that three consecutive declines signal the coming of a recession, but few analysts regard that as a certainty.

Including the component involving the length of the work week, eight of the index's 10 major categories showed adverse performances in April. The only positive contributions came from stock prices and the growth of the money supply.

The drop in new factory orders brought the total for the nation to $141.09 billion. The dip, the largest in more than four years, added to earlier signals that the economy is slowing.

The report also confirmed preliminary estimates late last week that new orders for durable goods - another key economic barometer - had fallen sharply in April. The figures showed the dip at 8.5 percent, from 8.7 percent before. CAPTION: Graph, Leading Economic Indicators, The Washington Post