Control over the $4 billion the federal government allocates annually for urban revitalization has seesawed over the years between Washington and local governments. Now President Reagan wants to shift the power back to city hall.

The plan to give mayors and county executives far freer rein in determining how federal Community Development Block Grant money ought to be spent is moving through Congress and the bureaucracy under the banner of the president's "economic recovery program."

It is based much more, however, on a controversial article of the Reagan philosophy that state and local governments, because they are "closer to the people," can direct urban revitalization and other federally funded social programs better than bureaucrats in Washington.

Few would disagree that local governments understand their problems better and that the present system of running the program from Washington has led to confusing directives, entangling red tape and long delays in gaining approval to spend the money.

But the question of critics is whether, in fact, local governments can be trusted to carry out national objectives if left to their own devices. Critics are concerned that no-strings money from Washington might be used as revenue-sharing grants to plug gaps in local budgets or be showered on the well-off when the aim of Congress is to help the poor.

The General Accounting Office, for one, is urging Congress and the administration to tighten -- not relax -- controls over the community development block grant funds. And the GAO just spent time in the field, examining how city halls spend the federal dollars they receive.

GAO's review of programs in a sampling of 15 cities across the nation, including Alexandria, Chicago, Minneapolis, San Diego and Newark, found federal dollars intended for upgrading blighted neighborhoods were being spent on ice skating and music lessons and construction of garages, sundecks and patios.

Funds Congress said should be spent with "maximum feasible priority" to benefit the poor and lower middle class were being used in one city for housing renovation loans to some families making more than $30,000 a year.

A spokesman for the Department of Housing and Urban Development said, in response to questions about the GAO survey, that while there may be some problems in some local programs, HUD believes the vast majority of communities have used the money for good and effective programs. The GAO report, the spokesman said, will not affect efforts to shift greater authority to local officials.

HUD Secretary Samuel Pierce has ordered aides to cut federal housing regulations by 15 per cent and he is asking Congress to reduce the role of his department and expand the authority of local governments.

The Community Development Block Grant program started in 1975. It replaced several former redevelopment loan and grant programs, including urban renewal, model cities open space, urban beautification and water and sewer grants.

An idea of the Ford administration, the program was designed to end the need for local governements to apply to Washington for revitalization funds on a project-by-project basis. Instead, about 660 cities and urban counties are given grants on the basis of a formula that takes into account the extent of poverty and overcrowded housing in a community.

Communities have used the money for a range of activities, including parks, playgrounds, water and sewer facilities and rehabilitation of homes.

The redevelopment funds are being used for to build the Emory Grove recreation center in Montgomery County and to renovate homes on Bates Street in downtown Washington, the showpiece of Mayor Marion Barry's housing renewal efforts. Sidewalks on streets off Benning Road in Northeast Washington and along Piney Branch Road in Takoma Park also are being repaired with the funds.

Pierce's proposals have been applauded by Republicans on Capitol Hill and by former Ford administration officials who see them removing a web of restrictions that hampers local governments in administering revitalization programs.

Warren H. Butler, a HUD deputy assistant secretary in the Ford administration, told a Senate subcommittee he did not believe the best renewal programs would result from "an endless array of national standards and requirements."

"I also do not accept the idea that the way to the heavenly city is through a computer in the basement of the Treasury Department issuing checks to eligible cities," he said.

Some Democrats and representatives of community and neighborhood organizations here have decried the proposals.

"Really now, what [the program] becomes is a revenue-sharing pot," said Milton Kotler of the National Association of Neighborhoods. "It will be used by cities to get rid of the poor."

Recent history provides many examples to support either Butler's or Kotler's point of view.

Local government officials in the Washington area, for examples, have complained of delays of up to two years in getting approval to spend renewal money because of requirements for public hearings, environmental impact statements and the like.

On the other hand, there is ample evidence that many local governments, left on their own, will stray from the intent of federal law. In 1975 and 1976, the first two years of the program, only about 10 percent of the money spent across the nation went for revitalization projects in the neighborhoods where the poorest one-fourth of the population lived. That was slightly less than the amount spent in areas where the wealthiest quarter of the population lived.

When GAO queried a cross-section of federal and local officials on their interpretation of the requirement that the money be spent with "maximum feasible priority" to benefit low- and moderate-income persons, half said the term had not been defined, was not definable, had little meaning or no meaning at all.

After that survey, the Carter administration added more rules and regulations, leading to the cries now heard in Congress about stifling red tape.

One of the added provisions gave a strong role in monitoring programs to community groups. Author Nick Kotz has argued that their work has been at least as valuable in scrutinizing local programs as that of university professors who are most often called on to evaluate federal efforts.

Community groups representing the poor were responsible for bringing to the attention of federal officials the fact that Birmingham was using money on a middle-income neighborhood while ignoring poorer communities.

They blew the whistle on the program in Evansville, Ind., where $130,000 in redevelopment funds was spent on the Community Development Block Grant office while some neighborhoods were unable to get renovation funds.

In the changes Pierce is proposing, federal requirements for citizen participation would be substantially curtailed. The community groups are also concerned about Pierce's proposal allowing the money to be used for loans and grants to businesses.

HUD spokesmen said they envision that money would be used to help neighborhood businesses such as mom-and-pop groceries that might need repairs or want to expand. They acknowledge, however, that the change they are seeking would be broad enough for bigger downtown businesses to qualify for funds.

If local governments misuse the money, Pierce has told congressional committees, HUD will move against them after the money is spent.