Builders started single-family houses in March at the fastest one-month pace since the government began to keep records in 1959, according to figures released yesterday by the Department of Commerce.

Single family homes were started at an annual rate of more than 1.5 million in March. Over all - including homes and apartments - new housing units were started at an annul rate of 2.1 million. That was the fastest monthly rate since May 1973, when the rate was 2.3 million.

The march pace is up substantially from February, when the rate was 1.8 million units. Housing units were started at only 1.4 million-unit rate in January, because of the severe cold weather which hindered outdoor work of all kinds.

Michael Sumichrast, chief economist for the National Association of Home Builders, said the big jump in housing starts was "more than we'd hoped for." Sumichrast said it looks like 1977 may be the best year ever for single-family housing construction.

The boom in housing construction has been delayed in the current recovery from the 1974-75 recession. Housing is usually among the first sectors of the economy to pull out of a recession and helps stimulate the rest of the economy.

But this time, the recession in home building continued long after the many other parts of the economy improved. No one knows for sure why the home building behaved differently this time, but most think it was because of the high cost of housing continued high inflation and a very slow decline in long-term interest rates.

Permits to build houses, an indication of future construction activity, also climbed smartly to an annual rate of 1.7 million units, up from 1.4 million units in February and 1.3 million in January.

Although the Commerce Department adjusts housing start data to account for normal seasonal variations there are often more dramatic swings in these statistics than in most other series reported by the government.

One government economist said that the March figures were "hard to believe."

Courtenay Slater, chief economist for the Department of Commerce, said that some of the big increase in March may represent starts that were deferred in January because of the freeze.

She said the level of housing starts in March is higher than she expected, but said that overall the numbers look good.

While home building is booming, other forms of construction - especially plant construction - is still lagging. The deficiency in plant construction is a reflection of general business unwillingness to make big increases in capital expenditures. Businessmen say that the lag in capital investment - consumer spending and inventory stocking have proceeded at about the pace economists expected from past recoveries - is due to a fear of rising inflation.

Price increases are much lower than in 1974, when double-digit inflation rocked the economy, but at a rate averaging nearly 6 per cent - and much higher than that in recent months - inflation is greater than in most periods since World War II.

The Carter administration is counting on an acceleration of plant and equipment spending 1977 to bosst overall economic growth. The administration's estimates of an 11 per cent increase in capital spending are considered too high by most economic forecasters.