The government's index of leading indicators dropped 2.4 percent in May, adding to the evidence that the economy's decline is slowing but that the recession is still far from over.

The index is supposed to foreshadow economic trends.The April index showed a record decline of 4.8 percent, but yesterday's figures revised this to 4.1 percent. However the March fall in the index is now put at 2.4 perent, somewhat more than first reported.

William Cox of the Commerce Department said the May decline "suggests that together with the large decline in Arpil there are still further cutbacks in industrial production ahead of us in the next few months." He said the further drop in May -- the seventh in the last eight months -- was not surprising. "We all know we are in recession" he said.

However, many private economists now believe that the worst of the recession could be over. Michael Evans of Evans Economics here said yesterday that he expects May's decline in the leading indicator to be the last for a while. The government's lastest forecast of the economy, to be released in about three weeks, probably will show that the economy suffered its biggest drop in gross national product in the quarter that has just ended. Economists now believe that the GNP fell at an annual rate of 7 percent or 8 percent in those three months.

The Commerce Department figures also showed that the ratio of the lagging indicators to the "coincident" indicators rose last month for the first time in several months. This ratio sometimes signals turning points in the economy. However Cox said yesterday that one month's figures are not enough to suggest reliably that the economy is turning around. The sharp rise in unemployment as a result of the recession will continue for some months.

Layoffs in manufacturing industries jumped sharply in May, according to figures published yesterday by the Labor Department. These showed that 3.5 percent of all manufacturing workers received layoff notices during the month. This is the highest figure since March 1958, showing that the layoff rate in this recession is worse than in any of the previous three.

The Labor Department said yesterday that the report points to further rises in unemployment from the 7.8 percent level reached in May. The June unemployment report, which will be released Thursday, could show a jobless rate as high as 8 percent of the work force.

The high layoff rate was the major factor pushing down the leading indicator last month.

Robert Gough, vice president of Data Resources Inc. of Lexington, Mass., agreed that "we still have severla more months of negative news, particularly on the industrial production and unemployment front." However, he found the rebound in the leading indicators from the dramatic April fall "comforting".

Other comforting news came yesterday from the survey of consumer confidence by the Conference Board. For the first time in eight months consumer confidence has improved. The Board's Consumer Confidence Index rose by nearly six points in June to reach 48 percent of its 1969-70 value. More than 15 percent of the 5,000 households interviewed last month expect business conditions to improve in the next six months compared with only 9.5 percent in May. The rise in consumer sentiment still leaves the index way below the October level of 83.6 after the record declines in April and May.

Lower inflation has helped boost consumer spirits but food prices are likely to accelerate in coming months. Average farm prices rose by 1.3 percent last month, following a revised 1.3 percent gain in May. Farm prices had fallen in the two previous months. However the Argiculture Department pointed out that despite the recent increase, prices in June were below their level of a year earlier for the fifth consecutive month.