Cash registers are ringing less briskly at stores around the United States - one of a number of signs that the US economy is cooling off. In March, retail sales dropped 2.2 percent, according to a new Commerce Department report. It was the second straight decline in retail sales and the sharpest one-month plunge since December 1973. Despite the decline, March retail sales still were 10.2 percent ahead of March '83 levels.
''The retail numbers are a clear indication that the consumer sector is slowing down and that the overall economy is slowing from what was a very torrid rate of growth,'' says Elliott Platt, senior vice-president and economist at Donaldson, Lufkin & Jenrette, a brokerage house.
There are other signs the economy is slowing. In March, for instance, sales dipped at new-car dealer showrooms. Car sales in March were at a seasonally adjusted annual rate of 7.9 million units, down from February's 8.5 million-unit sales pace. And the March unemployment figures showed a plunge in the number of new jobs the economy is creating. Statistics due out soon, including industrial-production numbers scheduled for release today and the housing-start report due Tuesday, are expected to confirm the trend.
''We see a significant slowing this quarter,'' says Jesse Abraham, an economist at Data Resources Inc., a forecasting firm. His company estimates that inflation-adjusted gross national product (GNP) - the value of all the goods and services produced in the economy - will rise at a 4 percent annual rate between April and June vs. a 7.3 percent gain in the first quarter of 1984.
''A slowing has begun,'' adds Donald Straszheim, vice-president of Wharton Econometric Forecasting Associates. ''When we get the March numbers over the next week or two there will be substantial evidence of that.''
The less robust growth has a variety of causes, including higher interest rates, less unfulfilled consumer demand for big-ticket items like cars and appliances, and a slight erosion in consumer confidence. Other factors that typically occur in a recovery, such as a change in business inventory patterns, are also at work.
Business investment in new factories and equipment will take up some of the slack left by more cautious consumers, economists say. Business spending for new plant and equipment and to rebuild inventories ''will be the leading edge of the expansion,'' notes Edward Friedman, senior economist at Chase Econometrics, another forecasting firm.
But because consumers account for roughly two-thirds of total demand, the economy is expected to slow as 1984 moves on. For example, Chase economists say they expect inflation-adjusted GNP to slow steadily as 1984 progresses and in the last quarter of 1984 to rise at a 3.7 percent annual rate, a pace three percentage points slower than what Chase expects the revised first-quarter-1984 growth rate to be. And many economists expect growth to slow even more in 1985.
The changed pace will have a mixed impact, forecasters say. Slower growth will take some upward pressure off interest rates and inflation, although neither is expected to plunge.
There are several reasons interest rates are not expected to drop sharply, analysts say. For one thing, the Federal Reserve Board has recently moved to tighten the supply of credit to the economy. Then, too, ''credit demands swell as an expansion matures,'' writes Edward Yardeni, senior vice-president at Prudential-Bache Securities Inc.
As recoveries progress, businesses typically have used up their excess cash and have to step up borrowing to pay for capital spending.
Slower growth also puts less upward pressure on prices. But as the economy continues to grow and move closer to full use of the nation's factories, both material and labor costs can be expected to climb, adding to inflation, forecasters say.
''Inflation will accelerate; it always has in every other expansion,'' Mr. Friedman says. But the upward movement in prices will not be as pronounced as in the period 1979-81, he says. Chase expects the consumer price index to rise steadily throughout 1984 and end the year at a 6.3 percent rate.
The retail sales numbers are ''a good sign that shows a leveling off of the recovery'' and provide evidence that the economy is not overheating, according to White House spokesman C. Anson Franklin.
But the slower growth rate is expected to produce some politically sensitive results. For example, further cuts in the unemployment rate may be harder to come by. In March the economy produced 250,000 new jobs, down sharply from the 700,000 created in February.
''Reductions in unemployment from here on out will be harder to achieve, in my judgment,'' says H. Erich Heinemann, chief economist at Shearson/American Express Inc. The jobless rate, which remained unchanged in March at 7.8 percent, may drop one- or two-tenths of a percent by year's end, he says.
And economists also expect the housing industry, which provides a large number of jobs and is very visible, to cool somewhat.
Housing starts, which were running at a red-hot seasonally adjusted annual rate of 2.2 million in February, will probably come down to the 1.8 million or 1 .9 million level in March, due to rising interest rates and other factors, says James Christian, chief economist at the US League of Savings Associations.