Housing starts rose 5.8 percent last month after a very sharp fall in February, the Commerce Department reported yesterday.

But permits for future housing fell by 3.2 percent in the month to an adjusted 1.128 million annual rate. The drop in permits came on top of a February fall of 5.1 percent in future permits.

The 5.8 percent increase in housing starts in March left them at an annual rate of 1.28 million units, 23.5 percent higher than a year earlier, the Commerce report said.

Thomas R. Harter, chief economist at the Mortgage Bankers Association, said the March rise was not a signal of a trend. Higher interest rates since last fall have dented the housing market, although not to the extent of last year's recession. In February, housing starts plunged by 26.9 percent.

In a separate report, the Federal Reserve Board said that there was little change in factory capacity in March. The nation's factories operated at 79 1/2 percent of capacity, after seasonal adjustment, the Fed reported, compared with 79.4 percent in February.

In March 1980 the overall operating capacity rate was 82.8 percent, the Fed said. The economy apparently continued to grow in the first quarter of this year, although many economists expect a slowdown soon. The unchanged factory utilization rate suggests a flattening in expansion.

The Commerce Department said that starts of multifamily residence rose by 10.9 percent in March to a 467,000 annual rate. This followed a 36.9 percent drop in February and left March starts 13.3 percent up from a year earlier.

Starts for one-family houses rose by 3 percent in March, after a 20.1 percent decline the previous month.

The drop in permit for future housing was 1.8 percent for one-family houses and 5 percent multifamily houses, the Commerce Department said.

The housing market is very sensitive to the level of interest rates, and Harter said he though that the March rise in starts reflected builders using financing arranged earlier when rates were lower. This might lead to easier financing but to cheaper house prices, he said.