By 40 to 37 percent, Americans give President Carter positive marks on his handling of the case of Dr. Peter Bourne, his adviser on health and drugs who recently resigned.

By 76 to 14 percent, Americans think that "President Carter did what he had to do -just as soon as he found out about illegal drug usage in the White House, he cracked down on it." When articles began to appear saying that some White House aides might have used marijuana and other illegal drugs, Carter promptly warned that any employes inclined to continue such practices could expect to be fired.

By 56 to 35 percent Americans agree that "wherever young people work these days, there is always the possibility they will use illegal drugs, so the reports about White House staff members using illegal drugs are being blown way out of proportion."

Moreover, by 85 to 9 percent, they think that "President Carter should be judged by what he accomplishes in office far more than by th persaonl habits of some of his staff members."

There are, however, a number of residual doubts in the aftermath of Bourne's resignation, as shown in the results of a recent Harris poll of 1,153 adults nationwide.

By 55 to 35 percent, a majority thinks that "when President Carter warned his staff they would be fired if they used illegal drugs, it sounded as though he might have a drug problem with his own staff." Here Americans seemed to be voicing their suspicion that use of illegal drugs have taken place among White House staff members.

In general, Americans are not very enthusiastic about Carter's White House staff. By 68 to 22 percent, they give the president negative marks on "the caliber of his appointments of close aides and advisers in the White House."

But Americans are not terribly upset by this state of affairs, and by 52 to 36 percent, they reject the charge that "the Carter White House staff has never been that good in the first place, and now the reports of illegal drug use there are just too much to take."

By 61 to 32 percent, they favor "an official investigation by the Justice Department of the possible illegal use of drugs by White House staff members." However, this step is seen by most as a fail-safe moev, rather than an action arising from a deep conviction that the Bourne episode revealed serious breaches of public trust.

At this point, the Bourne case does not spell serious trouble for Carter, although other disclosures might change that. Given the troubles that have beset the president, his problems lie elsewhere than in charges of illegal druguse in the White House.