Local governments in the Washington area have enough financial strength "to survive a moderate recession without undue strain or peril," a regional research center reported yesterday.

The Center for Municipal and Metropolitan Reserach said the District of Columbia would be hit hardest by an economic downturn. Unlike its suburban neighbors, which get state aid, the District itself must finance the kind of welfare, medical and housing costs that rise sharply during a recession, the center noted.

All local governments would face some drop in tax revenues and some rises in costs, the center declared in a 40-page report.

The center said the District of Columbia and Prince George's County, alone in the region, face "potentially serious special financial problems" as they look to the future.

It listed these as the uncertainty of federal support for D.C. and the restraints of the tax-limiting TRIM amendment added by the voters to the Prince George's charter. It said both make it difficult to plan future government outlays.

Philip M. Dearborn, vice president of the center and author of the report, pronounced the region's six major local governments to be financially healthy.

Things are so stable generally, Dearborn told reporters, that "my first inclination was not to publish [the report] because it didn't seem to serve much purpose to say things are okay . . . but it does tell something about where we are."

While not predicting the future, Dearborn said the area's governments have been able to deliver a high level of service to citizens because of a buoyant economy, political decisions that kept tax collections in line with resources and changed population trends -- including a sharp drop in school enrollments.

Between 1970 and 1978, total regional enrollment dropped 16 percent, from 608,160 in 1970 to 512,854 in 1978. The declines ranged from 32 percent in Arlington and Alexandria to 3 percent in Fairfax County.

If the higher enrollments had continued, Dearborn calculated, the region's school costs last year would have been $189 million higher than they actually were.

"It may well be that the relative school savings made possible . . . $77 million in new operating [subsidy] funds for Metro," Dearborn speculated. "New spending of this magnitude would ordinarily have been difficult [without such savings]."

Dearborn reported these other findings:

The rate of spending by all area governments rose sharply from 8.1 percent in 1977 to 12 percent in 1978, while revenues slacked off from 14.8 percent to 11.6 percent, "not a desirable trend."

While area governments have increased long-term debt for construction projects by 15 percent in the last three years, greater tax receipts resulting from the sound economy have kept this from being burdensome. The region's tax-supported debt totaled $2.3 billion last year.

While individual family tax burdens may differ slightly at various income levels, "the area as a whole has . . . no very high or very low taxing jurisdictions." At the $30,000 level, the range from the highest (District of Columbia) to the lowest (Arlington) tax burden is only 1.9 percent.

While Dearborn did not advocate any tax policy change, his report noted that D.C. "is unable to capitalize fully on its economic growth" because its charter prohibits taxing suburban incomes. Congress has sidetracked city proposals to repeal that ban.

Between 1974 and 1976, the report said, personal income earned by all persons working in the city rose 19.5 percent, while city income tax collections "increased by a mere 11.5 percent."

The city's problems in its financial relationship with the federal government are twofold, Dearborn said. The city is forced by the congressional appropriation process to keep its books "on a generally discredited basis" that sometimes indicates solvency when there really is not enough cash to pay all the bills. And, he noted, the level of the annual federal payment to the city is so uncertain that it hobbles fiscal planning.