Industrial production declined sharply in April, while housing starts edged downward, giving more evidence that the economy is cooling off.

Much of the 1 percent drop in the Federal Reserve Board's index of industrial production - which measures the output of the nation's factories, mines and utilities - was due to the effects of last month's trucking strike. Analysts said the strike seriously slowed production of automobiles, trucks, auto parts and steel.

However, the fall in industrial output - the first since early 1978 and the largest for one month since February 1975 - was widespread, and some economists think it is likely that the economy slowed somewhat in April. The index rose by a revised 0.7 percent in March, the Fed reported.

Housing starts slipped to a seasonally adjusted annual rate of 1.749 million units last month, the Commerce Department said. That was only 2 percent below March's level of 1.786 million, but 20 percent below last year's level.

In March, housing starts had recovered significantly from the weather-depressed levels of January and February, and some experts, including Kenneth Biederman, chief economist for the Federal Home Loan Bank Board, had expected another substantial gain in April.

On the basis of the sales of existing homes, as well as conversations with builders around the country, Biederman had been looking for a level 100,000 units or so higher than the reported 1.749 million.

Biederman was puzzled by the regional pattern of starts, with most of the decline concentrated in the South. In any event, he said that "without one heck of a rebound in May and June, there is no way that starts will average 1.7 million for the year, which we have been forecasting."

Housing permits also declined last month, dropping by about 100,000 units at an annual rate, another sign that housing construction will slow further this year.

The head economist for the National Association of Home Builders, Michael Sumichrast, who has predicted a sharp decline for the year, judged the April performance "quite respectable."

"It should be about the same this month, but things will get tougher beginning in June and for the rest of the year," he added.

The biggest reason is that mortgage money is becoming harder to get in some parts of the country and more expensive everywhere.

The nation's savings and loan associations had an $800 million net outflow last month, and mutual savings banks lost about$700 million. That is the first month since 1974 that the S&L's, which provide most of the housing credit, had more withdrawals than deposits.

Meanwhile, economists at the United States League of Savings Associations predicted that the tightening of savings flows, coupled with continued strong demand for mortgage money, will push mortgage interest rates to 11 percent or more by fall.

Kenneth Thygerson, the group's chief economist, said that rates already have hit 11.25 percent in California and could reach 11.5 percent there and in some other states.

In terms of industrial production most analysts believe it will be late May or early June before the key statistics are free enough of the effects of the trucking strike to indicate how the economy is performing.

The April decline brought the overall industrial production index to 150.5 percent of its 1967 average. Output now stands 5.1 percent above a year ago.

The impact of the trucking strike was substantial by any measure. Auto assemblies plummeted an extraordinary 16 percent to an annual rate of 7.9 million units - far more sharply than had been expected.

Output of consumer goods fell 1.8 percent in April following an 0.7 percent gain in March. Production of consumer goods fell 6.4 percent, while manufacture of nondurable goods rose a scant 0.1 percent.

Output of business equipment and of materials both fell 0.7 percent in April following increases of 0.9 percent in March. All of the Fed's figures were adjusted to compensate for seasonal patterns. CAPTION: Chart 1, INDUSTRIAL PRODUCTION; Chart 2, Housing Starts