Federal investigators first became suspicious of 10-year-old Jose Martinez when a computer at the Health and Human Services Department spat out his name.

According to the computer, Jose's mother had been receiving welfare checks for more than four years, yet she had never filed a Medicaid claim for her son. There was no record that Jose had ever visited a doctor for treatment of a virus, an earache or a broken bone.

Howard Pierce, the HHS agent who investigated the case, said, "It just didn't seem right." It wasn't. Pierce's investigation revealed that Jose Martinez existed only in welfare records and in the minds of Louis and Angela Lopez.

The Lopezes pleaded guilty last year to charges that they created Jose, along with nine other fictional children, to qualify for extra welfare benefits. Over four years, they illegally collected $60,000 by using three aliases and the fictional children.

What makes the Lopez case unusual, however, is not how they cheated the government but how they were caught. Their ruse was uncovered during an ambitious HHS operation now being tested in Connecticut. Called "Project Missing Kids," it uses "computer matching" to detect fraud.

In the last year, the government has launched more than a dozen similar projects in which one agency compares its computerized files with another agency's. In the missing-kids project, for example, welfare records were compared to Medicaid tapes to identify children who had never incurred any medical expenses. Those names were then compared to public school enrollment records to see if the children existed.

Computer matching has been so effective at detecting fraud--recovering an average $7 for each $1 spent--that President Reagan's Council on Integrity and Efficiency has created a separate Long-Term Computer Matching Committee to encourage more computer investigations.

The committee will promote computer matching, study how federal and state records can be tapped--including confidential records like federal income tax returns, and review current laws that restrict computer matching.

The administration is pursuing the idea vigorously because it has had such success with it over the past year. For instance:

* The Veterans Administration compared its list of uncollectable accounts with the federal government's master personnel file. The result: 66,454 federal employes were identified as owing $36 million to the VA.

* HHS asked the Labor Department to compare its Black Lung Benefit accounts in six southern states to HHS Medicare tapes. The result: six Kentucky hospitals were accused of double-billing the federal government for $660,000 in medical treatment.

* Suspicious that immigrants had applied for duplicate or additional Social Security cards that later were given or sold to illegal aliens, the Social Security Administration and Immigration and Naturalization Service compared computer tapes. The result: 50 convictions and 800 aliens deported.

* The Agriculture Department checked the reported income of food stamp recipients in Tennessee by comparing data from USDA, the Housing and Urban Development Department and state unemployment offices. The result: $3.7 million in suspected overcharges, 203 indictments and six convictions.

The government has 58 different programs that pay benefits according to an applicant's income, explained Thomas F. McBride, the Labor Department's inspector general and co-chairman of the computer committee. "Computer matching is the most efficient way to ensure that only the deserving get benefits."

There is some concern, however, that in their zeal to uncover fraud the investigators may skirt some of the constraints of the Privacy Act of 1974 and subsequent guidelines issued by the Office of Management and Budget for computer matching. Moves are under way to review and modify the "more burdensome and less effective" parts of the guidelines, according to Richard Kusserow, the inspector general at HHS and the committee's other co-chairman.

John Shattuck, national legislative director for the American Civil Liberties Union, believes matching could lead to "enormous invasions of privacy" by allowing the government to make a "general search of records and then target specific people." Without the match, investigators would have to show "probable cause" and obtain search warrants before launching such investigations, Shattuck said.

Shattuck also says matching lends itself to abuse. "What happens if the government decides to match its list of federal employes against domestic security files compiled by the FBI in the 1960s when it was investigating anti-war and civil rights activists?" he asked.

Before an agency can perform a computer match it must negotiate with other agencies what information will be swapped and how it will be used, guarded and destroyed. Once an agreement is reached, it must be published in the Federal Register and Congress and OMB notified.

The committee has not yet said how it wants to change those requirements, but it argues that the process slows down investigations, sometimes by as much as 60 to 90 days after two agencies agree to swap information.

Hugh O'Neill, a privacy-act expert at HHS, said the committee is only interested in "making the rules consistent with our technology. We are talking about streamlining the system here, not throwing away the safeguards. We intend to be public and keep our cards on top of the table."

McBride and Kusserow said they feel matches that involve confidential government records could be performed without violating the privacy of honest Americans. For instance, McBride said, banks currently tell the Internal Revenue Service how much interest individual taxpayers earn on their savings accounts. "No one's privacy is violated by that government safeguard," he said.

Congress voted last year to let states send the names of parents who are behind in child-support payments to the Social Security Administration and IRS. Those agencies check the names against their records. If the parent is due an income tax refund, the IRS intercepts it and contacts the state child-support agency.

"No one is talking about creating one huge, 1984-style data bank of information about all Americans," said James E. Foster, director of advanced computer techniques at HHS, which has done more computer investigations than any other agency. "Law-abiding citizens will have nothing to fear."