The Commerce Department's index of leading economic indicators declined 0.2 percent in April, signaling a continued slowdown in the economy.

The index, which serves as the government's main gauge of future economic activity, reflected a continued weakness in the industrial sectors of the economy while the service sector remained strong.

The Commerce Department revised the March index to show a 0.1 percent increase. The government earlier had reported a decline of 0.2 percent that month.

Many economists predicted yesterday that despite poor growth in the first half of the year, activity would probably pick up later as interest rates continue to decline and income tax refunds delayed by computer errors at the Internal Revenue Service give consumers more money to spend.

In a separate report, Commerce said sales of new single-family houses fell 11.9 percent in April to an annual rate of 612,000 units. The drop followed a 5.5 percent rise in March, Commerce said.

The April sales rate was the lowest monthly level of single-family home sales since December 1984, Commerce said. Sales have been down 3.4 percent during the first four months of 1985 from sales during the same period last year.

"Our economy has been in a temporary lull, with much of the recent sluggishness reflecting a poor performance in goods-producing industries," said Commerce Secretary Malcolm Baldrige. He said consumer confidence and spending both improved last month, and housing starts have been strong in recent months.

Wharton Econometrics said it expects growth this year compared with last year to rise at a rate of only 2.6 percent, in contrast to the 6.8 percent rate in 1984.

The Reagan administration is in the process of refining its estimates of economic growth. Baldrige said several weeks ago that he doesn't expect the economy to grow as strongly as the administration's goal of about 4 percent.

"What the indicators show basically is that the economy is muddling though and it will probably continue muddling through through the summer," said David Berson, an economist with Wharton Econometrics. By the end of August or beginning of September growth should start bouncing back, Berson said.

Allen Sinai, chief economist for Shearson Lehman Brothers, said the manufacturing sectors are in a mild recession, but that the recession wasn't enough to pull the entire economy down.

One key indicator -- new orders for plant and equipment -- declined in April for the eighth time in the past 11 months. This indicator usually gauges future expansion of business capacity. However, much of the equipment business has gone to imports because the strong dollar has made imported goods cheaper than those made domestically, economists said.

The decline last month in the plant and equipment indictor "was the third-largest in that indicator in the last 11 months," Sinai said. "That indicator reflects the siphoning off of capital goods orders abroad."

A recession is unlikely because the goods sector, which seems to be having the hardest time in the expansion, has become a smaller part of the economy in recent years and the impact of lower interest rates will show up in housing and automobile sales. However, a turnaround in the dollar's strength is needed for any substantial improvement, Sinai said.

The indicators that contributed to the decline were contracts and orders for plant and equipment, the money supply, the average workweek, building permits, and net business formation and vendor performance, which measures the speed at which deliveries are made to business, reflecting the demand for goods.

Indicators that were positive were new orders for consumer goods, sensitive materials prices, stock prices and initial claims for state unemployment.