In a large public school in Brooklyn earlier this year, about 50 children who had been getting free or low-price lunches were fed leftovers from other students' trays instead. All qualified for a federally subsidized meal but couldn't get it because their parents hadn't filled out a complex, new government form.

"Some of the parents didn't understand it and some didn't want to fill it out because they thought it was rather personal," said Charles Buchanan, assistant principal at P.S. 219. "The old form did not ask for the number of household members, it did not ask for all their Social Security numbers, it did not say, 'List all persons related and nonrelated who live in the household and share living expenses or meals and then give the Social Security numbers of this group.' "

From its first days in Washington, the Reagan administration has heralded its desire to streamline rules and reduce paper work, producing hit lists of regulations it considered unnecessarily onerous. Administration figures show that last year paper-work requirements for Americans dropped 13 percent--or 200 million hours annually.

Yet one kind of red tape is just as knotty as ever: the paper work encountered by poor and middle-income Americans who receive federal aid for food, housing, higher education, medical costs or utility bills. Paper-work requirements, said an administration official, are one way to make sure the aid goes only to those who need it.

"There's no doubt that there's an inherent contradiction between two objectives of this administration," said Edwin L. Dale Jr., chief spokesman for the Office of Management and Budget. "One objective is to reduce paper work. The second is to focus means-tested programs on those who really need them. In some cases, the paper-work objective has had to give."

The rules encountered by people in these benefit programs serve "a different objective," Dale added. They are designed in part to properly target government aid and counter waste and abuse. "The savings will be in the hundreds of millions of dollars," he said.

This fiscal year, the federal government will pass out about $65 billion to at least 23 million people with incomes below various legal limits. Because of changes put in place by Congress and the Executive Branch in the past year, many of the people receiving federal aid--welfare recipients, college students with federally guaranteed loans, some public housing tenants--now must provide more information or update forms more often to get the aid.

Even more people will encounter more paper work if Congress adopts some new administration proposals--if they qualify at all under new lower income ceilings or rules that now count as income assets that were once disregarded.

One of the programs most tied up in new red tape is Aid to Families With Dependent Children, the basic $14 billion welfare program in which the federal government has a $7.1 billion share.

Recipients must now report their financial status to their local welfare office monthly; in 32 states this process used to take place twice a year. And a new "retrospective" budgeting system will increase by weeks the time lag between when a recipients' outside income drops and when his welfare payments are boosted. An increase in outside income will still trigger an immediate drop in welfare benefits.

One staffer of the Center for Social Welfare Policy and Law complained that complications in paper work and the removal of safeguards to help welfare recipients who might be illiterate, retarded or non-English speaking could "disqualify for procedural reasons people who are otherwise entitled to aid."

All tenants in federally subsidized housing must soon provide proof of citizenship or resident alien status because of new rules excluding some foreigners; elderly tenants will soon have to report their financial status once a year, twice as often as before.

College financial assistance offices must now do a "needs analysis" if the family income of a student receiving a federally guaranteed loan exceeds $30,000; in April, if Congress approves, that analysis would have to be done for all 3.5 million participants in the Guaranteed Student Loan program, a program through which Uncle Sam helps pay the interest on loans and makes good on defaults.

Thanks to 1981 budget reconciliation legislation, more of the students in the Pell grant program--a $2.3 billion program that provides annual grants of up to $1,670--must have their financial status verified by their college. The Education Department has drafted--but not yet proposed--new rules that would require the families of these 2.8 million students to submit income tax returns along with grant applications next year.

"In general, we've seen an increase in the amount of regulation in both grant and loan programs over the past two or three years," said Dr. Dallas Martin, executive director of the National Association of Student Financial Aid Administrators.

Rule changes and the new reporting burden on aid recipients inevitably translate into more work for the people who pass out the money. "There's more work to be done trying to explain to the students what's going on," said Robert Huff, Stanford University's director of financial aid. "There's a great deal more paper work for us and a great deal more hassle for the poor," said Camille Wheeler, director of the Baltimore County welfare office.

The amount of paper work involved in filing for federal aid varies from program to program. An AFDC recipient must complete a form giving his name, address, Social Security number, age, marital status and family size; he must also report and verify his rent payments, and detail his assets and their value: cars, bank accounts, insurance policies, stocks and bonds.

The paper-work requirements for some benefit programs have not changed much. These include the $17.9 billion Medicaid program, which helps pay health costs of nearly 23 million people, the $11.3 billion food-stamp program, which serves about 20.5 million Americans, the $7.9 billion Supplemental Security Income program, providing assistance to 4.1 million people who are blind, elderly or disabled, and the veterans pension program, providing $4.1 billion to 2 million people.

However, a new monthly reporting requirement like the one for AFDC recipients has been proposed for food-stamp recipients in 1983.

Since the rule changes have not become final, subsidized housing tenants have seen little change in paper work. The complications to come, however, may be exacerbated if Congress adopts the administration's proposal to count food stamps as part of a tenant's income.

"When you try to restrict eligibility for these programs, an increase in the paper-work burden on applicants and recipients is almost a given," said David Racine, government affairs director of the American Public Welfare Association. " . . . If the federal government wants to limit access to these programs it has to be willing to pay the price . . . . Part of that cost is the increased administrative burden on state and local governments, the other part of it is the burden that falls on recipients."