The 6,000 children who are detained in the District's three youth facilities each year are given poor medical and psychiatric care and are often locked up for hours because of insufficient staff, according to a summary of depositions given by District officials in connection with a lawsuit filed by the Public Defender Service and the American Civil Liberties Union's National Prison Project.

The lawsuit, which is set for trial July 7, is one of several legal problems facing the District's Youth Services Administration. The agency, which operates the city's facilities for troubled youths, is under federal investigation for possible contract fraud, obstruction of justice and widespread payroll irregularities in which nearly 100 of the agency's 420 employes doubled their salaries through overtime payments, some of the money being paid for time that apparently was not worked.

The agency's director, Patricia Quann, was forced to resign May 30, and Mayor Marion Barry described as "incredible" the agency's $1.3 million in yearly overtime. In the days after Quann's resignation, three top administrators were put on leave in order for a two-week internal investigation to be conducted.

The summary of the depositions, which was made available to The Washington Post by a source who is not a party to the lawsuit, contains statements made this spring by officials with the Youth Services Administration and the Commission on Social Services, and by private consultants.

The depositions concern the care of children held in the city's detention facilities for delinquent youths -- Oak Hill and Cedar Knoll, both in Laurel, and the D.C. Receiving Home for Children in Northeast Washington.

According to the officials and consultants, the youths in the city's care are neglected and their housing is unsafe and deteriorating. The buildings are poorly ventilated, heated and maintained, and some staff members refuse to ride in agency vans and buses, claiming they are unsafe, according to the summary.

District officials have echoed many of these complaints in testifying before budget hearings. In the midyear budget, $483,000 was appropriated to correct many of the physical problems cited in the lawsuit.

Supervisors reported that a shortage of staff members results in guards who are "short-tempered and not very understanding." In some cases, children were handcuffed to beds without necessary approval from a doctor, the summary states.

Edward A. Mahlin, deputy director of Oak Hill, said, "[You] have men who are tired and irritated and aggravated because they've been working too damn much."

Slapping of children happens in cottages because of the strain of overwork, according to the summary. Supervisors reported that some staff members showed up for work high on drugs or alcohol. However, because of staff shortages, few disciplinary actions against staff were taken.

Mahlin added, "We've got kids being locked down because we only have one man and the union contract says he doesn't have to work with 20 kids." As a result, there are frequent "mass lockdowns" for four hours of the eight-hour shifts, he said.

Security consultants Eric Swinn and Walter C. Farrier said that a "potentially explosive situation" existed in September 1985, as Quann had "lost control of scheduling procedures and disciplinary procedures involving line staff." They found that staff members at Cedar Knoll and Oak Hill were taking advantage of personnel shortages by scheduling themselves for overtime and taking sick time for their days off.

Barry said that 60 new staff members, about 30 of whom have been hired, will help alleviate the overwork and overtime problems.

Barry blamed many of the agency's problems on the city's inability to close one facility, Cedar Knoll, because of an increase of children with drug charges being sentenced to city custody.

Although the facility is no longer carried on the budget and it changed its name to "Annex" last December, it is filled to its 100-bed capacity. Its students must be transported to the nearby Oak Hill facility for school, and all of its staff and medical help must be borrowed from other facilities.

Barry said last week he wants to meet with Judge Ricardo Urbina, presiding judge of the District's family division, to discuss ways to decrease the number of children being sent to city facilities.

But Urbina is the judge assigned to hear the Public Defender Service's lawsuit against the city, and defender service director Cheryl Long last week sent a letter to the corporation counsel objecting to the mayor's request for a meeting. The city's lawyers have not responded, and no action has been taken on the mayor's request, according to the judge's staff.

The summary of depositions states that:

*Despite an announced crackdown on drug usage at Oak Hill, guards have not been searching the staff for drugs because employes object to being patted down.

*Despite an increasing number of children with drug charges, there is little drug treatment or counseling at the institutions.

*As of this spring, there was no medical help at Oak Hill and Cedar Knoll on the weekends, no sign-up sheets for children needing medical help, and inadequate emergency medical transportation. One staff doctor said he had complained to Youth Services officials for years about the serious problems in medical care at city youth facilities.

*The youth facilities lack medical equipment and do not perform routine medical, hearing and vision tests on children. Children given blood tests often are released before the four weeks necessary for test results to return from a lab at D.C. General Hospital.

*Rodents were found throughout the Receiving Home for Children, especially in the kitchen.

*The three facilities have serious fire safety deficiencies, including the fact that children sleep in locked rooms with no central switch to open doors in an emergency.

Quann, before she resigned, said the agency was attempting to correct many of the deficiencies cited in the lawsuit. "Many of our problems are common to most jails in this country," she said.