Private schools and voluntary organization throughout the Washington area that serve clients under contract with the District government have been driven to financial desperation by the city's inability to pay its bills on time.

Schools for handicapped children, social service agencies, and health and housing organizations say they have gone for months without payment. they have been forced to borrow money, defer salary payments, and in some case make unauthorized transfers of funds earmarked for other programs in order to keep operating.

Some schools and agencies, dependent upon their monthly checks from the city, have not been paid since September. Estimates of the amount the city owes them for their services range upward from $3 million -- a trifling sum in a $1.5 billion city budget but a fortune to organizations that have to scratch for every dollar.

City officials acknowledge that payments have lagged. They say the problem is not a shortage of cash but the complex process of recording the service contracts in the city's computerized auditing system, without which checks cannot be issued. Staff shortages and computer breakdowns have impeded the process. By the end of last week, oficials in Mayor Marion Barry's office, the public school system and the Department of General Services, which does the actual proessing of the information, said they believed the problems had been solved, but the cash-short schools and agencies still were not getting their money.

"It's happening across the board, it's endemic," said James Kalish, director of the Washington Council of Agencies, an association of voluntary and comunity organizations in the city. "It' affects hundreds of organizations. We operate under a crisis mentality."

"It's not any one department, it's all of them," said Michela Perrone, executive director of the Kennedy Institute and president of the D.C. Assocation of Independent Special Education Facilities. "Every member of the association has this problem. The question is what we can do about it. How can we get this system to work?"

She said that her school, the Kennedy Institute, which provided education and job training for the retarded and handicapped, has 55 students who were referred by the D.C. public schools because they cannot be trained in the regular classroom and 15 others referred by the Department of Human Services for a total of 70 the 90 enrollees at the school. The annual tuition fee for each, she said, is $5,960, payable in monthly installments.

"We don't have a big endowment," she said. "We don't have a cent except what we collect as we go." The only payment her school has received from the District government since September, she said, was an emergency allotment to pay January salaries, a day after they were due.The school official, former finance director James R. Boyle, confirmed her account.

Other agency and school directors told of incidents like these:

The Metropolitan Washington Planning and Housing Asociation was forced to borrow $14,000 at 2 percent above the prime rate last Friday to cover commitments that were supposed to have been met out of District Disbursements. The prime rate was 20 percent at most banks on Friday.

At. St. Gertrude's School, a small school in Brookland run by the Benedictine order of nuns, the diredtor, Sister Luann, said she was using money provided by Maryland to cover expenses for the five D.C. children enrolled there. "We aren't totally dependent on the District because Maryland pays in advance for the semester," she said. "But what it means is the city is getting interest on our money. You can call all the administrators, but it's always one thing or another. They told me it was coming, but nothing has happened.

The director of an agency that provides treatment and counseling for alcoholics and receives funds from several sources said she diverted money from a United Way grant to cover a program operated under a city contract. She asked that neither she nor her agency be named.

At Christ Church school in Bethesda, where children with severe learning disabilities are educated at a cost of $610 a month, director Sheri Gelman said the is $77,000 in arrears. "We have a contract," she said, "but they have not paid in any month since September."

Workers at other organizations told of members of boards of directors who made personal loans to their agencies to tide them over, of deferred salary and vendor payments and of appeals to banks for informal, interest-free loans to meet current expenses.

Kalish said that no other jurisdiction in the area has the same difficulties as the District in paying its social service contractors. He said that some kind of "crisis intervention system" is needed to provide emergency funds to those agencies that need quick infusions of cash. He said he had recommended to city officials that agencies be reimbursed for the cost of borrowing. "I'm not optimistic that we can do more in the short term than apply these band-aid solutions," he said.

Rung Pham, the acting finance officer of the District's school system, and Howard Schwartz chief of procurement at the Department of General Services, said that the complexities of the city's accounting system required a two-step process in which each separate contract must be negotiated by the appropriate city department and then recorded by General Services. The purpose of that is to centralize control over city expenditures, which it evidently does, but at the expense of quick payment to contractors. City Controller Al Hill, the official identfied by others as directly responsible for dealing with the problem, said, "I agree , there is a problem. If the contract is not posted, the checks cannot be issued. It's a built-in inefficiency, but we hope to get on top of it."