The Carter administration has picked James Hamilton, former assistant chief counsel of the Senate Watergate committee, to become administrator of the Law Enforcement Assistance Administration, reliable sources said yesterday.

Hamilton's selection caps a two-month search by Attorney General Griffin B. Bell for a new head of LEAA, which attributes federal crime-fighting funds to the states. The administrator's post has been vacant since the departure of Richard W. Velde on Feb. 26.

The sources said President Carter is expected to announce Hamilton's appointment as soon as the FBI completes a check of his backgound.

Bell has ordered a joint Justice Department - LEAA study group to examine the agency's operations and make recommendations whether it should be drastically reorganized or demolished.

LEAA, a semi-independent agency under the policy control of the Justice Department, was established in 1969 as the spearhead of federal efforts to combat street crime. It has distributed almost $6 billion to the states for research and support of local crime-fighting programs.

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

The agency has continually come under fire for allegedly wasting money on poorly conceived and ineffective projects. Its critics charged that LEAA funds too frequently have been used to buy expensive hardware for local police forces and finance grandiose programs that have had no impact on crime rates.

Hamilton, a native of Chester, S.D., served as chief deputy counsel for the Senate committee that in 1973 probed the White House cover-up of the burglary at the democratic headquarters in the Watergate office building in 1972.He was responsible for the committee's investigative work and its litigation in the federal courts.

Last year, he published a study of the congressional investigating process entitled "The power to Probe."

Hamilton is a partner in a Washington Law firm of Ginsburg, Feldman and Bress.

Also yesterday, Gerald M. Caplan, director of LEAA's research arm, the National Institute of Law Enforcement and Criminal Justice, announced his resignation effective May 6. Caplan is the last hold-over from the Nixon and Ford administrations ina policy making position at LEAA.