The District of Columbia, which is relatively immune from recession, is nevertheless one of the largest recipients of anti-recession aid from the federal government, according to a new study by the Treasury.

Moreover, instead of using this aid for special anti-recession programs, the District uses much of it to finance regular municipal services. The District is thus "hooked" on the anti-recession programs and would suffer if they are cutback on schedule as the recession recedes, the study says.

The District is not unique in these respects, the study adds. Many big cities have become heavily dependent on federal anti-recession funds and could suffer painful withdrawal symptoms.

Nor are the District and similarly situated cities-gluttons for the Federal dollar, according to the report. Nearly all of the cities, have declining tax bases, dwindling populations, slow economic growth and chronically high unemployment.

The District, for example, had a 7.1 per cent unemployment rate in 1976, when elements of the economic stimulus package were being put into effect.

But, the Treasury report notes: "The economic stimulus programs may have begun as aid-to-the-economy programs, but, in some instances, may have become aid-to-the-government programs, particularly for governments under sever financial strain . . . This . . . might easily lead to a reliance by the recipient governments, resulting in an 'ad hoc' federal assistance program"

This poses policy problems for the Carter administration, which wants to cut back on the anti-recession programs for fiscal and political reasons. The Treasury report does not make any recommendations. It simply describes the problem by looking at the impact the overall $15.8 billion economic stimulus program has on 48 of the nation's largest cities.

The District, for example, is one of the six largest per cpaita recipients of anti-reession money, taking in $120 September 1978, when the program is supposed to expire.

In overall economic stimulus money, the District is expected to receive $83.3 million. One out of every 14 of the District's city government jobs is federally funded, according to the report.

The report classified the 48 cities in categories of "High, moderate and low economic strain." The District is one of 28 cities listed in the "moderate" category.

Property taxes are one of several possible measures of the dependency of cities on federal economic stimulus funds. For example, cities in the "moderate" category might have to impose an average 40-cent increase (per $100 of full market value) in property taxes to make up for money that would be lost if all of the federal anti-recession funds are taken away, the report said.

Cities in the "high strain" category might have to impose an average 65-cent increase per $100 of full market value and cities in the "low strain" category would need an average 24-cent increase to make up for the shortfall, the report said.

However, the report cautioned that the degree to which any city would be hurt by a withdrawal of the federal anti-recession aid would depend on how the city used the money when it had it, the city's ability to attract state financial support, and the exten; to which the city is willing to reduce services to make up for the reduction in federal funds.

Treasury officials said yesterday that the report is expected to play a major role later this year when Congress considers extending key elements of the economics stimulus anti-recession package. President Carter has already recommended that two parts of the program -- anti-recession revenue sharing and the Comprehensive Employment Training Act (the CETA public employment program) --be extended by $1.04 billion and $6 billion, respectively.

No extension has been requested for the $6 billion local public works program, which is supposed to help state and local governments finance specific construction projects. J. Chester Johnson, deputy assistant treasury secretary for state and local finance, said yesterday that cancellation of the construction program should have no effect on local governments "because the public works money was never used for government operation purposes."

"High strain" cities, those greatly dependent on the federal aid, are Boston, Buffalo, Chicago, Cleveland, Detroit, New Orleans, New York, Newark, Philadelphia, and St. Louis, according to the report.

"Low strain" cities, those least dependent on the federal largess, are Columbus, Denver, Houston, Memphis, Norfolk, Oklahoma City, Phoenix, Portland, Ore., San Diego, and San Jose, the report said.