The Internal Revenue Service will cross-check the name and Social Security number of every applicant for welfare, food stamps and Medicaid this fall for the first time in a search for unreported interest or dividend income that could make them ineligible for those programs.

The new "computer match" will be the broadest use of IRS information ever authorized by Congress for nontax purposes, other than routine statistical uses, according to Sen. William S. Cohen (R-Maine).

The IRS has historically tried to keep its records private. "If we make the IRS into an information lending library for government agencies, we are likely to undermine our tax system of voluntary compliance," said former IRS commissioner Donald Alexander.

Civil libertarians also complained that the plan threatens an invasion of privacy.

Congress ordered the IRS to participate in an income and eligibility verification system in 1984 as part of its effort to weed out ineligible beneficiaries and reduce the federal deficit. The checks are not intended to help the IRS find more income to tax, but to cut the cost of assistance programs by spotting people who are not disclosing all their income sources to welfare and other agencies.

The IRS eligibility checks are only part of the system. States are also required to check Social Security records to assure that applicants and recipients of Aid to Families with Dependent Children (AFDC), food stamps and Medicaid do not have unreported income or assets. States must also check unemployment claims against the wage data reported by employers.

Rules governing the verification system were published Feb. 28.

The Office of Management and Budget is also drafting legislation to add veterans benefit information, alien status and federal employe pension and employment information to the pool of data available to state and county welfare offices.

Computer matching has been used as far back as 1977, when the Carter administration compared computer tapes of welfare recipients with federal payroll files in several states to detect government employes who were fraudulently drawing welfare benefits. The major new element this year is the use of IRS information.

The Grace commission recommended expanding verification more than two years ago in its report on government waste. "If we are in a $200 billion deficit situation, and we are, we have to look at every penny," said George Goldberger, president-elect of Citizens Against Government Waste, the commission's successor organization.

"More effective prescreening of applicants will reduce error rates and better target precious resources to the truly deserving," said OMB Director James C. Miller III in publishing the final rules govering the mandatory system.

The OMB estimated that the new rule will save $375 million in 1987, according to a chart distributed by the Congressional Budget Office, which estimated in 1984 that the implementation of a verification system would save $350 million in 1986.

The new use of IRS data has raised questions of privacy.

"While we have to be concerned about fraud and waste in government programs, I have concerns that the privacy of citizens may be shortchanged as we release more tax information to state agencies," Cohen said in a statement. "While matching has been going on at the state and federal levels, I think average citizens would be amazed to know how widely records are exchanged without their knowledge," he said.

"We think that it is a breakdown of the principle of the confidentiality of tax information and an intrusion on privacy," said Jerry J. Berman, director of the privacy and technology project of the American Civil Liberties Union. "We do not doubt that the government has legitimate purposes in reducing fraud and cheating. But how far should we move from an individualized system under which the government checks up on one individual suspected of cheating to a system of random ongoing surveillance of millions of citizens to see who is cheating?"

Under the new system, states will make a tape of the names and Social Security numbers of applicants for AFDC, food stamps and Medicaid and mail it to the IRS. Once a month, the IRS will run each state's tape against its master tape of information about interest and dividends. The IRS will mail the tapes back to the states with the information about each "match" -- how much unearned income the person received.

"The system is designed to ensure that state or local caseworkers will have no direct access to federal records," an OMB spokesman said.

Some state welfare departments checked recipients against Social Security records as early as 1980, but states will now be required to check information on anyone applying for AFDC, Medicaid and food stamps. State unemployment insurance agencies will now be required to use wage records to help identify persons who collected unemployment benefits while employed.

The law establishing the verification system requires independent verification of fraud before benefits can be terminated, and entitles recipients to a hearing.

The new verification system, known among welfare officials as SIEVS -- for statewide income and eligibility verification system -- is part of a larger network of computer data bases available to government agencies.

In California, for example, the state checks tax records to make sure that recipients are not concealing wealth from their county welfare officials. The District of Columbia, Maryland and Virginia already have automated systems that check for unreported wages and certain assets. They conduct periodic computer checks of each other's records to detect double dipping.

The President's Council on Integrity and Efficiency said that more than 1,200 state computer matches have been conducted with sources ranging from wage records to lottery winner files.

"To improve verification . . . program managers are establishing more and more links with other assistance programs," the General Accounting Office said in a report.

IRS files are often considered the most sensitive of all government records. Former IRS commissioner Alexander said, "I am sympathetic with the goals [of the new verification system], but I think this is a poor way of achieving them.

"The problem we have is that the more the IRS information is spread around the block of government agencies -- agencies without the IRS tradition of concern for privacy -- the more likely tax return information would be discussed around the neighborhood."