For the second time in as many weeks the D.C. school board has failed to approve a proposed agreement between the city and the school system that would end years of dispute over the placement of handicapped students in private residential facilities.

Under the agreement the school system would be responsible for paying for educational services in a private facility for public school students who require 24-hour supervision because of their handicaps.

The city Departments of Human Services would be resonsible for paying the room and board in most cases and the entire cost of medical, psychiatric and social and vocational rehabilitation services for these students.

The proposal is significant because it reflects the first time the city has agreed to pay for noneducational services for any handicapped student. Previously, the city agency was paying for the residential placement of only those students who were also wards of the court such as juvenile delinquents and orphans.

The school board first deferred action on the agreement to seek suggestions from the public. Then, when some citizens had a chance to offer recommendations -- most of which were critical of the agreement -- the board decided to delay action again until it received these recommendations in writing.

When the proposed agreement came before the board at a meeting on Tuesday, the board tabled it.

Most of the criticisms of the agreement came from lawyers who represent parents in a current class-action suit against the school system over its special education programs. These parents alleged that both the department and the school system have wrongfully refused to place their children in private facilities because neither agency could agree on which one should pay for the placement.

In 1971 a U.S. District Court judge ruled that all handicapped children have a constitutional right to public education and that the shool system must place them in private programs when there are no appropriate programs for them in the public schools.

At a hearing Tuesday attorney Michael Eig, who has several clients in the class-action suit, maintained that the agreement, if approved, would delegate too much authority to DHS over the educational placement of a handicapped child.

Eig called the vagueness of the agreement "an open invitation to even more litigation" and charged it "sets up another means for delay -- what I call the Ping-Pongism of students going back and forth between the school system" and DHS.

Eig said he was not objecting the school system's sharing responsibility for the handicapped child with DHS but that the "ultimate responisibility" must rest with the school system.

Sue Wynn, a parent and activist for handicapped children, told the board she was concerned that the agreement did not address where parents can go to appeal the residential placement their child receives. One of the major complaints of parents of special education students is that the children are often placed in inappropriate programs.

Members of the public will have until Friday to submit recommendations to the board in writing. Superintendent Vincent E. Reed said he will not guarantee the system will incorporate their suggestions into the agreement.

The full board is scheduled to take final action on the agreement at a community meeting Wednesday.