An analysis just released by the Metropolitan Washington Council of Governments appears to give further credence to the theory that the region's economy is no longer recession-proof.

Although the COG findings are based on an analysis of leading indicators in the final quarter of 1981, the conclusion is significant in that it tends to dispel a myth about the region's economy.

Indeed, the COG report concludes: " . . . It appears that the Washington region is equally experiencing the effects of national recessionary trends and has become less resilient in recent years."

COG bases its finding on an analysis of selected national and regional economic indicators, which showed similar performances.

And, said COG, the region's economy experienced a "marked slowdown" during the final three months of 1981 when compared with the performance of indicators in the comparable period a year earlier.

It's not clear what has happened to the region's economy since the first of the year. An analysis of economic indicators for the first quarter of this year probably won't be completed for another two to three weeks, according to Noora Ahmed, an economist at COG.

However, since there appears to be a pattern in which regional indicators have been tracking national barometers, it's possible that the economy in metropolitan Washington continues to experience a slowdown.

What emerged in the final quarter last year, COG said, is a "combined result of slowed economic growth as well as the implementation of the economic recovery policy designed to balance the federal budget by reducing the level of federal employment and federal spending."

Total nonagriculture employment in the region increased only one percent during the last three months of 1981, compared with a 4 percent gain in that period a year earlier.

Meanwhile, the unemployment rate rose a full percentage point to 5 percent.

Figures compiled by COG show that the region's public sector lost 14,000 employes in the final quarter last year, more than three-fourths of them federal employes.

During the same period, COG reported, the nation lost 231,000 public employes, 16,000 of them in the federal sector.

And although much has been made in recent years of the fact that the area's economy is less dependent on the federal government, job losses in that sector have had a telling effect. More than 75 percent of the federal job losses nationwide were concentrated in the Washington region, according to COG.

The fact that government's share of regional employment has gradually declined over the years "reduces the region's ability to resist severe national recessionary trends to the extent that it has in the past," COG economists say.

From its analysis of regional employment patterns of the past, COG concluded that total employment remained fairly stable during the last two short post-World War II recessions. However, there was a "substantial drop" in the region's total salaried employment during the 1973-75 recession.

During that same period, COG said, employment in the goods-producing industries declined substantially when the construction industry lost 22,000 employes.

However, employment in the government sector rose substantially, offsetting the loss of 19,000 jobs in industries such as retail/wholesale, finance and real estate, transportation and communication.

A summary of findings based on the performance of regional economic indicators in the final quarter last year shows:

* Effective mortgage rates for new homes rose from 14 percent a year earlier to 18 percent in the last three months of 1981.

* Construction activity measured by the value of building permits issued declined more than one-third, from $105 million to $77 million.

* Retail sales increased by only 3 percent, substantially below the inflation rate.