At least 36 persons, most of them prominents Rhode Island citizens, have resigned parttime positions on state government agencies rather than disclose their personal finances as they are required to do by a new state conflict of interest law.

The law, which was approved by the state's General Assembly in 1976 and went into effect in January, has also prompted two lawsuits by persons seeking to overturn the statute's disclosure provision.

Similiar conflict laws, which exist in some form in 36 states, were heralded last year by proponents of the Rhoda Island law as important steps to ensure confidence in government that had been shaken in part by Watergate.

About 3,200 persons complied with the law's reguirements by filling financial statements by July 1 or by reguesting an extension. Conflict commission officials were pleased at most 3,400 officals are covered by the law.

The Rhoda Island law is administered by a state conflict-of-interest commission. The statute's provisions apply to local as well as state officials. The law is considered a tough one ans includes a section listing activities prohibited to public officials.

Among the prohibitions: public officials may not do business with the state unless there is an "open" bidding process.

While other specifics of the prohibited-activities section have yet to be adopted by the conflict commission, some observers expect this section to spark even more controversy, and perpahs resignations, than the disclosure requirements.

For now, however, it is the financial-disclosure aspect of the law that has prompted the estimated 36 resignations and left Gov. J. Joseph Garrahy with the task of finding replacements.

Two state sgencies have been put out of business, temporarily at least, by the wave of resignations. Four of the five members of the Industrial Building Authority, with is responsible for attraction new industry to the state, have guit. And all four members of the Board of Examiners in Optometry have left rather than disclose.

The law requires public officials including these part-time officials who have been resigning, to list such things as sources fo occupational income and certain stock and property owned. It doesn't require specific dollar amounts, but rather only the disclosure that a person owns a minimum of 10 per cent of $5,000 worth of a company.

Still, those who have resigned so far say they're quitting not because they 've got something to hide, but because of a belief that their basic rights of privacy are violated by the disclosure required.

"I don't think any court in the land would uphold the law [on privacy grounds]" said Marvin Holland, who resigned as chairman of the Howard Development Corp., a state authority responsible for developing an industrial park in the sity of Cranston.

In the latest of the six legal challenges to the conflict law. Superior Court Judge Ronald R. Lagueux this week denied a request for a preliminary injuction to block enforcement of the law against all state and local officials.

The injuction was sought by James F. Macdonald Jr., a member of the state Port Authority and Economic Development Corp.

Lagueux said he reasoned that those who had complied with the law's financial disclosure requirements were implicitly saying they did not want to be included in Macdonald's class action suit. The judge did, however, grant an injunction blocking enforcement of the law against Macdonald.