The key government index designed to predict turning points in the business cycle fell sharply in January for the third month in a row -- bolstering the view that the economy is beginning to slow down.

The Commerce Department reported yesterday its index of leading indicators plunged 1.2 percent in January after dropping 0.1 percent in December and 0.4 percent in November. The dip was the steepest in four years.

Although some analysts adhere to the thumbrule that three consecutive declines signals a recession, yesterday's figures were considered an exception. Much of the drop stems from a falloff in money-supply growth, which is considered necessary in the fight against inflation.

At the White House, Jody Powell, the president's press secretary, said key Carter economists regard the decline as foreshadowing a moderate slowing in the economy's growth rate. He said Carter still expects no recession.

Most non-governemnt economists agreed with that general interpretation of yesterday's figures, but many are forecasting a recession later this year -- and with a good deal more conviction than they were only a few months ago.

Yesterday, several private economists told the Senate Budget Committee a recession was likely later this year and early in 1980. They cited higher than expected inflation and the oil situation as contributing factors.

The figures came as the department reported separately that construction spending plunged 4 percent in January to a new level of $208.1 billion, providing still another piece of evidence that the industry may be entering a slowdown.

Although officials warned publicly against interpreting one month's figures as any sort of long-term trend, the dropoff was so large analysts said it almost certainly signals a downshift.

Figures on housing starts published last month showed a sizable falloff, to 1.6 billion, from a 2 million rate earier. Construction usually is the first industry to be hit when the economy slows.

Yesterday's figures on the leading indicators showed five of the 10 componets now available contributed to the decline in the index, while five moved in the opposite direction.

Besides the money supply, those components cited as negative included the length of the average workweek, building permits, change in liquid assets, and change in sensitive prices.

Those bolstering the index in January included the layoff rate, the number of companies reporting slower deliveries, stock prices, contracts and new orders for plant and equipment, and new orders for durable goods.

Meanwhile, the Federal Reserve Board repoted that the nation's basic money supply, comprising cash and time deposits, fell moderately again last week after growing bridfly in the two previous weeks -- allaying fears of an expansion.

The report showed the basic money supply, M-1, fell to a seasonally adjusted average of $358 billion in the week ending Feb. 21, from $360.2 billion the previous week. A broader measure, known as M-2, also declined, to $876.7 billion.

The January decline brought the index of leading indicators to 136.5 percent of its 1967 average. The figure, however, will be revised next month after late-breaking data are collected.

The thumbrule citing three consecutive declines as signaling a recession has been broken several times in recent years. The latest was in mid-1977 when the index dropped three time but no recession occurred.

In another development, Federal Reserve Board chairman G. William Miller said yesterday the dollar is eign exchange markets, despite the recent impact of higher oil prices.

The U.S. moved to stem the dollar's decline last November by raising interest rates here to lure back capital and by setting up a special fund to defend the currency in the markets.