The Washington metropolitan area's economic fortunes started improving at the end of 1982 and the beginning of 1983 after a year in which the total number of civilian jobs here declined by 8,300, the first such drop in at least 32 years, according to a study released yesterday.

The number of jobs in the metropolitan region increased in the last three months of 1982, after falling in each of the first three quarters, according to the report. Meanwhile, the number of housing construction permits issued by local governments jumped markedly in 1982's last quarter, and the area's unemployment rate dipped from last year's 6 percent average to 5.7 percent in February.

"There are some positive signs," said John C. McClain, an economic analyst for the Metropolitan Washington Council of Governments. "If this continues, it will be better for the Washington area than in '82.

"Recent indicators suggest that a national recovery is already under way," he told representatives of local governments on the COG board, "and there were several changes in trends for the Washington area . . . that suggest the effects are already being felt in Washington."

McClain suggested that the recovery in the Washington region also may be quicker than elsewhere, on the theory that "our private sector is not affected as much by the lingering effects of the recession because we're not manufacturing-based."

But McClain also presented a series of statistics and charts that debunked any notions that the Washington region may have been immune from the national recession. While the economic hardships were not as severe here, a variety of economic indicators showed that the recession and the Reagan administration's goal of reducing the federal work force left a toll of high unemployment, reduced construction spending and stable retail sales after figures were adjusted for inflation.

He said that from 1977 to 1980, the number of jobs in the 16-jurisdiction Washington area increased by 188,000. By contrast, the number has grown by only 2,000 since then.

Since 1980, the Washington area has lost 27,000 government jobs, most of them in the federal work force as President Reagan's budget trims have been implemented and some federal programs eliminated. McClain said that in 1981 the increase in employment at private firms in the Washington area offset the loss in government jobs, but that last year the number of private jobs increased by only 6,500, while the number of government jobs declined by 14,800.

McClain said that COG has records on the number of Washington-area jobs dating back to 1950 and that last year's decline of 8,300 was the first time that a loss in jobs had been recorded.

While the number of available jobs was declining, unemployment was increasing, from an average of 86,000 persons out of jobs monthly in 1981 to 102,000 last year. But McClain said that the figure had dipped to 96,700 by February, the last month for which statistics are available.

Moreover, he said that in the fourth quarter of last year, the number of Washington-area jobs increased by 5,500 over the same three-month period in 1981, the only such increase last year over 1981. The fourth quarter also showed the biggest 1982 gain in the number of private jobs and the smallest decline in the number of government jobs.

In addition, the number of housing construction permits increased from 14,041 in 1981 to 16,340 last year, with nearly one-third of the authorizations being issued in the last three months of the year.

The inflation rate for the Washington area declined in 1982 for the second straight year, to 5.3 percent, down from the 1980 high of 11.9 percent.

As in recent years, the dollar volume of retail sales again increased in 1982, to a total of $19.1 billion. But when the figures are adjusted for inflation, retail sales in the Washington area have remained virtually constant since 1978.

The value of new construction in the Washington area last year totaled $2.57 billion, a slight drop from the $2.72 billion figure of 1981, the report said.