Retail trade dropped by 1.3 percent in December, breaking a six-month trend of rising sales, the Commerce Department said yesterday. Much of the decline was in sales of autos and parts, but there was also a slight downturn in business for department stores, drug stores and gas stations.

"I suppose you could read it as one bit of evidence that the economy is slowing," said Commerce economist William Cox yesterday. However, he cautioned that the advance report of sales often is revised and should be interpreted with care.

Businesses have reduced their investment plans for this year, according to another report from Commerce yesterday, but they still plan to spend more on new plant and equipment than they did in 1980. Nonfarm business in the United States is expected to show a 10.8 percent rise in investment in 1981 before allowing for inflation. Last year's overall increase in capital spending on plant and equipment was 8.8 percent higher than in 1979, the Commerce report said.

In real terms, after accounting for inflation, the department estimates that capital spending fell by about one-half percent last year and will rise by 1 1/2 percent this year. Given the amount of unused spare capacity at the moment, and the fairly dim outlook for growth this year, the business survey suggests relatively "healthy" investment, Cox said.

Retail trade last month was 5 percent higher in nominal terms than a year earlier, representing a fall in real terms after accounting for inflation. y For 1980 as a whole, retail trade totaled $942.5 billion, a 6 percent gain over 1979. If autos are not considered, then trade last month increased 7 percent from a year ago and little changed from November.

Most analysts are expecting the economy to slow down this year, even if there is not a full-fledged recession. The swift climb of interest rates last month and the dent in incomes from a rising tax burden this year are cited as reasons for a slowdown.

But there ae still precious few signs that the downturn has begun. In the absence of these, financial markets recently have sent money rates up again after their fall early this month. For the short term there is an "upside risk" on interest rates, according to Chemical Bank economist and Senior Vice President Frederick W. Deming yesterday. But Deming had been expecting a rise in retail sales last month on the basis of cheerful sales reports from stores for the Christmas period.

One other indication of coming weakness in the economy is that the money supply, on the narrower measures, has been falling for the last five weeks, with steep drops recorded in the last two weeks in December.

Last spring a plunge in money stock was one of the first harbingers of the steep fall in the economy. At the time, the figures were treated gingerly as the money supply series is not reliably linked with real economic activity, such as gross national product growth or industrial production.

Some economists argue that the money figures in the summer again signaled early what was happening to the real economy, when they grew more rapidly than expected, and that the December drop in money will turn out to be a reflection of a faltering of growth. But many are still wary of pinning much on the movement of the money numbers alone.

Other December indicators will be scanned keenly to see if they suggest a slowdown. The unemployment figures, published last week, still reflected growth in the economy. Industrial production, due to be published tomorrow, will be looked at closely to see if they add to the evidence of the money supply declines and weaker retail sales.

Manufacturing industries now plan a 14 percent spending increase in 1981, the Commerce survey showed. This, though higher than the average rise in business investment, is below the 16 1/2 percent increase last year. In durable goods industries, large increases are planned by electrical machinery manufacturers (30 percent) and other machinery producers (18 percent), with much smaller investment rises predicted by automakers (8 1/2 percent) and a fall of 8 1/2 percent foreseen by iron and steel firms.