Weeks before unsubstantiated rumors about Michael Dukakis made their tortuous way into print, the political apparatus of Bush campaign manager Lee Atwater was investigating the details and trying to spread the findings without leaving any vice presidential fingerprints.

The target was to trash Dukakis without hurting Bush. Typically for a maladroit campaign, the result was the opposite on both scores. But unlike Dukakis, his own strategists and nearly the entire journalistic community, the vice president's men privately insist that the case is not closed nor the last word heard.

Reluctance to let the incident drop confirms that this was no trivial excursion but a vital tool in the quest for the world's most powerful elective office. Republicans are beginning to doubt Bush's ability to become the first presidential election winner to erase so large a polling lead. They are coming to feel that the political destruction of Dukakis is necessary for Bush to win.

Highlighting Dukakis' liberal record may energize conservative activists but can scarcely capture soft Dukakis supporters. In seeking an office where character counts more than in any other political contest, it is becoming an unspoken Republican tenet that the stability and credibility of the governor of Massachusetts must be undermined.

Thus, rumors long extant about two instances of depression by Dukakis attracted the Bush campaign's interest long before they were spread by Lyndon LaRouche's minions. Because Atwater's ''opposition research'' could not risk being caught, his lieutenants asked outside Republican operatives to do the digging and then quietly broadcast whatever they might find.

Nothing came of this. Atwater himself was reputed to have measured the reliability factor of the Dukakis rumors at between 10 percent and 20 percent. The principal Bush hope rested on a rumored Detroit News story which had not yet run but which Bush operatives believed would contain information about visits by Dukakis to a psychiatrist friend who was also a neighbor of Kitty Dukakis' sister.

Dukakis himself fanned the flames with his July 29 refusal at a Springfield, Ill., press conference to release his medical records. The Boston Globe, the only major news outlet to report it, buried the refusal deep in a routine campaign story. But that was enough to create the first real crisis for nominee Dukakis.

What happened the next 48 hours was a phenomenon peculiar to the insiders' political community: obsession with a question utterly unknown to the rest of America. Bush headquarters alerted key Republicans across the country to the forthcoming Detroit News story, arousing feverish speculation that actually suggested Dukakis might be forced off the ticket. Democratic politicians, fearing a combination of Geraldine Ferraro and Thomas Eagleton, wondered what there was in Dukakis' medical record that seemed to preclude its release. Lurid accounts of bizarre illnesses proliferated.

But in Boston, an Aug. 1 high-level Dukakis strategy conference spent 45 minutes on the convict-furlough issue, utterly ignoring the medical records crisis. That might have been either underemphasis of rising tension or recognition by Dukakis' managers of the stubbornness of a doctor's son about releasing his medical records.

The long-awaited Detroit News story appeared on Aug. 2 and was a bitter disappointment to the Bush camp. Apart from revealing a new Dukakis refusal to release information, it contained nothing fresh. There was no word about the psychiatrist, who a few days later told reporters he had never counseled Dukakis on any basis, formal or informal.

The fast-dying story was revived by President Reagan on Aug. 3 with his reference, in answer to a LaRouche magazine correspondent's question about medical records, to Dukakis as an ''invalid.'' It was not planned, but sources would not deny that the president did intend to break the story open. Apart from his half-apology, Reagan was unrepentant (perhaps reflecting Nancy Reagan's fury over Dukakis' crack at her husband that when a fish rots, the rot starts at the head).

With the story in the national spotlight for the first time, Dukakis finally released a brief, nonspecific medical report of the kind candidates usually issue -- as had been urged for days by campaign chairman Paul Brountas. The incident seemed to end with a classic backfire, Dukakis apparently unhurt and the Bush campaign linked to Lyndon LaRouche.

But key Democrats were unnerved by Dukakis' performance. Assuming he told the whole truth with nothing to hide, the risky delay in releasing his medical history demonstrated stubbornness, ineptitude and a touch of arrogance.

The vice president's men are determined the affair has not ended. They seem determined to extract something out of an embarrassing, losing incident. This determination is driven by their fear that it will take more than conventional politics to beat Michael Dukakis.