The Justice Department is considering whether the Law Enforcement Assistance Administration, which has distributed almost $6 billion in crime-fighting funds to the states, should be drastically reorganized or abolished.

Department sources confirmed yesterday that Attorney General Griffin B. Bell has ordered appointment of a joint Justice-LEAA study group to examine the controversy-plagued agency and make recommendations about its future.

LEAA, part of the Justice Department, was established in 1969 to serve as the spearhead of the Nixon administration's much-publicized war against street crime. Its principal function is to channel federal money to the states for research and support of local crime-fighting programs.

That gives LEAA the biggest share of Congress's annual appropriation for Justice Department activities. LEAA's budget for the fiscal year that ends Sept. 30 is $753 million, or 32 per cent of the Justice Department budget.

The FBI, which accounts for the second-largest slice of the department's budget, now has a budget of $513 million.

Throughout its history, LEAA has come under constant fire for allegedly wasting money on poorly conceived and ineffective projects. Its critics charge that LEAA funds too frequently have become a "pork barrel" device for local police forces to buy expensive hardware and finance grandiose projects that have had no impact on crime rates.

Since becoming Attorney General in January, Bell has repeatedly made clear that he is dissatisfied with LEAA's performance. Justice Department sources say Bell was especially upset when he learned, shortly after taking office, that the agency was going to spend $2.5 million on a brochure telling local police departments how to apply for LEAA funds.

The Attorney General has said several times that he regards reform of LEAA as one of his top priorities. He also has said that his chief reason for choosing former Pittsburgh Mayor Peter F. Flaherty as deputy attorney general was a desire to enlist Flaherty's administrative expertise in reshaping LEAA.

One of Bell's first acts was to fire former LEAA Administrator Richard W. Velde and his two top deputies. Since then the agency has been marking time under the temporary direction of James M. H. Gregg, a career employee who heads LEAA's office of planning and management.

In the meantime, Bell has been engaged in an extensive search for a new administrator. Reliable sources say that at one point it seemed certain the job would go to Herbert Sturz, director of the Vera Foundation, a private, nonprofit New York organization that does research on criminal justice problems.

However, the negotiations with Sturz were suddenly put on the back burner, Department sources say they do not know whether that means Bell has decided to delay naming a new administrator until he has the recommendations of the study group.

In a semi-facetious reference to President Carter's plans for restructuring the federal government's budget justifications, one department source refers to the study group's task as "zero-based agency review."

That, other department sources explained, means that LEAA will be examined in terms of what it's supposed to be doing, what its past and present programs have done to achieve its goals and what can be done to close the gap between the agency's purpose and its performance.

The result, the sources added, could be a recommendation that LEAA and its programs be abolished. It could also mean a recommendation to eliminate LEAA itself, while continuing to supply federal crime-fighting funds to the states through special revenue-sharing programs.

However, many department sources say it is doubtful that LEAA will be abolished. The agency, they note, has strong support from governors and municipal officials, who are fearful of losing a key source of federal funds, and this backing is reflected in Congress, which would have the last word on whether to abolish LEAA.

The likely outcome, the sources say, will be an attempt to make LEAA more manageable and efficient by a wholesale reduction of its 55,000 programs.

The aim, according to the sources, would be to de-emphasize LEAA's old hard-sell billing as an organization capable of eliminating crime as a national problem. Instead, it would focus on a drastically limited range of problems, where the impact of its programs would be susceptible to measurement.

The sources said the proposed study group is to be composed of three officials from LEAA and three from the Justice Department, who will work in tandem.

Most sources expect the project to be headed by Walter Fiderowicz, a special assistant to Bell. However, they said, decisions on the membership and direction of the study group have been held up pending the arrival at the Justice Department of Flaherty, who is scheduled to be sworn in next week.