Arlington County officials proposed yesterday a stringent $207 million budget for the next fiscal year that would reduce county services and trim the number of county goverment employes, but require no increase in the real estate tax rate.

The budget recommendations, made public by Acting County Manager Anthony H. Griffin, amount to a 2.6 percent spending increase above the current fiscal year, far less than the present rate of inflation. Griffin attributed the tight financial plan for the fiscal year beginning July 1 primarily to the Reagan administration's cuts in federal aid and to the current economic slump.

The County Board, scheduled to complete action on the budget proposals by April 24, is expected to face tough choices. Either the board must accept cutbacks in popular government programs, officials said, or vote to raise taxes--a move it already has tentatively rejected.

Board Chairman Stephen H. Detwiler yesterday described the proposed budget as a "very reasoned" document, and said he was not yet prepared to suggest modifications.

One key issue--the amount of county spending for the Arlington school system--remains to be settled through future talks between County Board members and education officials. The board has suggested $47.5 million in county spending for schools next year, but school officials have proposed as much as $50 million in local spending.

Under the budget proposal, county employment would decline slightly by about 23 jobs from the current total of 2,314 employes. Anton Gardner, county director of management systems and budget, said the employment cut would save about $1 million and would be carried out solely by attrition -- voluntary retirements and resignations, rather than layoffs. In addition, county officials have previously suggested eliminating another 50 county jobs.

The budget proposal provides for a 5 percent increase in cost-of-living allowances and fringe benefits for county employes--a sharp drop from the 9.1 percent cost-of-living raise granted last year.

The county Department of Human Resources "continues to be the most affected by the changes in federal funding levels," the proposed budget says. A series of cuts in social welfare services are proposed. These are partly offset, however, by a $1.8 million increase in federal funds for refugee assistance. "Without this increase," the proposed budget notes, "DHR's total budget would have reflected a $591,591 decrease from fiscal year 1982."

The spending plan includes a suggested 22.6 percent reduction in pay-as-you-go outlays for construction and other capital improvements, a decrease from $3.1 million this year to about $2.4 million next. The reduction would eliminate plans for a new fire department training center and other projects, including sidewalks, landscaping, bus shelters and street lighting.

County officials said they expect federal aid to be cut by more than $4 million next year compared to the 1981 fiscal year. This year, officials said, the county has already dealt with about $3.5 million in Reagan administration cuts, largely by eliminating programs. The county, however, has used about $500,000 of its own contingency funds to keep some services in operation despite the federal reductions, officials said.

The national economic downturn also has reduced Arlington's real estate tax collections, which brought in about $1.4 million less than previously forecast for the current fiscal year. County officials had expected real estate values to rise 14 percent, but assessments climbed only 10 percent, they said.

The county's real estate tax rate is 96 cents on each $100 of assessed value.