A computer check of welfare recipients' bank accounts in Massachusetts has uncovered one with $89,000 in the bank and others with $10,000, $20,000 or $30,000, Massachusetts officials said yesterday.

Families with more than $3,000 in the bank are prohibited from receiving food stamps, and the cutoff is less for recipients of general assistance and most other forms of welfare, officials say.

State officials ran the Social Security numbers of welfare recipients through the computers of 23 of the state's 1,013 banks and discovered 613 welfare clients with cash assets "beyond the limit required for eligibility" in six welfare programs. All told, the state found $4 million in undisclosed cash.

The findings, reflecting only cash and not cars, houses or household items, could have broad national implications if they hold up when all the banks in the state are surveyed. Massachusetts welfare officials say the figures suggest that more welfare clients have substantial assets than had been suspected.

One of President Reagan's major political themes has been the need to cut down on welfare costs by weeding out cheaters. Massachusetts Gov. Edward J. King also has stressed this goal, and he released the computer report in the midst of his race for renomination in the Democratic primary against former governor Michael S. Dukakis.

Massachusetts Human Services Secretary William T. Hogan said the computer check was carried out under a law on the books since 1967 but not used until now. "To the best of our knowledge, no other states have done this," Hogan said.

Hogan said the welfare officials sent the Social Security numbers of 547,385 persons, some of whom receive several different types of welfare, to 23 of the state's 1,013 banks in an effort to find out whether they had cash assets.

From those 23 banks, representing 2.3 percent of the banks in the state, Hogan said, the computers had pulled up 613 cases in which the welfare recipient apparently had cash assets in excess of the cutoff figures.

According to Hogan's figures, in 392 cases the individual had less than $5,000 in cash, but more than the amount allowed under the program in which he was enrolled. This varies from $250 for a person on general assistance to a maximum of $3,000 per household for those on food stamps and $3,000 per couple for Medicaid.

In 87 cases the account contained between $5,000 and $10,000. In 56 it had between $10,000 and $15,000. There were 26 in the $15,000-to-$20,000 range, 20 in the $20,000-to-$25,000 range, 14 from $25,000 to $30,000, five from $30,000 to $35,000, two from $35,000 to $40,000, five from $40,000 to $45,000, three from $45,000 to $50,000, one from $50,000 to $55,000, one between $60,000 and $65,000 and one at $89,000.

Hogan said the state had begun to attach the accounts to recover some of the welfare payments made to ineligible persons and would examine all cases for possible prosecution.

Hogan said the entire list of clients' Social Security numbers is being sent to the remainder of the banks in the state. If the results follow the same pattern as in the initial 23 banks, Hogan said, it is possible that substantial bank accounts might be uncovered for as many as 20,000 to 30,000 people. Hogan claimed that if the pattern were to hold true for the nation the preliminary Massachusetts results suggested that "the amount of potential excess liquid assets would be $6.9 billion."

Of the 613 cases, 157 involved Aid to Families with Dependent Children, 149 Medicaid, 163 food stamps, 61 general assistance and 83 supplemental supporting assistance.

Aides said a small sampling of these cases showed that the typical AFDC case among the 613 was a woman of 33 with two children, receiving $350 to $380 a month benefits, on the rolls about 56 months, with $13,400 bank assets. The typical food stamp recipient among the 613 was a woman of 60 with cash assets of $15,000 who had been receiving stamps for 30 months.