Productivity in U.S. business declined at a 0.9 percent annual rate in the second quarter, providing further evidence of a slowdown that economists in and out of government have been forecasting.

The fall-off between April and June followed a sharp 4.3 percent gain in the first quarter.

At the same time, it was reported that June contracts for new residential construction were down 5 percent from the previous month, but housing could be close to a modest turnaround if interest rates soften.

In its productivity report yesterday, the Labor Department said the second-quarter decline was caused by a 3 1/2 percent drop in output that was accompanied by a 2.6 percent decrease in hours worked.

Productivity, which measures how many goods and services the private economy produces in each hour of paid working time, declined at an annual rate of 0.4 percent in the fourth quarter of 1980, then registered a strong showing between January and March.

When productivity declines, rising wages cannot be offset by increased production. As a result, unit labor costs go up even more sharply, producing upward pressure on prices.

Lawrence Fulco, an analyst with the Bureau of Labor Statistics, said the second-quarter performance was characterized by "a decline in both employment and average weekly hours." Employment fell to 77.8 million and the average work week declined to 36.4 hours.

In the quarter ended June 30, the agency said, productivity in all ptIn the quarter ended June 30, the agency said, productivity in all private business, including farming, increased at a 1.1 percent annual rate.

The second-quarter decline in the nonfarm business sector occurred despite a strong showing in manufacturing, which registered a 4.2 percent gain on an annualized basis.

The department also revised its figures for productivity in nonfinancial corporations -- which excludes banks, stock and commodity brokers, and financial and insurance companies -- from the fourth quarter of 1980 to the first quarter of this year, saying productivity rose at an annual rate of 6.3 percent.

Meanwhile, sales of new single-family homes plunged 17.2 percent in June to the lowest level since the bottom of last year's recession, the government reported yesterday.

The new report by the departments of Commerce and Housing and Urban Development also said the average price of new one-family houses sold in June jumped $4,000 from May to a record $88,300.

The F. W. Dodge Division of McGraw-Hill reported that overall contracting for new construction rose 7 percent to $14.9 billion in June, but the gain was entirely due to contracts, totaling $1.1 billion, for two large fossil-fuel power plants.