By now most people know the story about the president and the rabbit. For those who don't, it seems the president of the United States was out in a fishing boat alone and was attacked by a ferocious rabbit. The president splashed his oar at the rabbit and drove it away.

When he got back to shore he told his White House staff about the incident, but they wouldn't believe him.

Now if this were just the story of a president and a bunny it would be none of the public's business. But the tale does have political implications, and it says quite a bit about Mr. Carter's way of running the White House.

In previous administrations it is hard to imagine anybody on the president's staff doubting the word of his boss.

If Presidents Truman, Eisenhower, Kennedy or even Nixon had said they had been attacked by a rabbit on a pond a staffer's reaction would have been "Thank God you're safe, Mr. President." Or in the case of President Johnson, Jack Valenti or Joe Califano would have said, "Please tell us about it, sir, and don't leave out one detail."

Even Jerry Ford's staff would have taken the chief executive at his word.

But such was not the case with President Carter. When he got back to shore with what he thought was a good tale to recount, his people refused to believe him.

As far as it could be learned, not one person said, "Well done, Mr. President. That rabbit will think twice next time before he attacks the leader of the most powerful country in the world, " or "If this doesn't show you can row and hit a rabbit at the same time, nothing will."

Instead he found nothing but skepticism when he related the story amongst his advisers and friends. Some insisted that rabbits could not swim; others doubted that, even if they could swim, they would attack a person holding an oar in his hand. Still others showed by their silence just how far morale in the administration had declined.

It is rumored that Ham Jordan had even considered giving everyone who worked for Mr. Carter a loyalty test to find out who believed the president's bunny story and who didn't.

President Catter, who never shows his emotions, was crestfallen. The credibility of the president had reached such a low point that, even when Mr. Carter said he had been attacked by a swimming rabbit, no one would take him at his word. Mr. Carter chalked it up to the malaise in the country that had now infected even his own staff.

Fortunately for Mr. Carter, a White House photographer, who was on a bluff overlooking the pond, had taken a picture of the battle. Carter showed the photo to his staff, who studied it, but they were still skeptical. Someone said, "It's an animal but how do we know it is a rabbit?"

For the first time since he took office Mr. Carter stopped smiling. He orderd Jody Powell to blow up the part of the photo that highlighted the thing in the water. Then he called in the staff again. "Well, is it a rabbit or isnt' it?"

They finally decided by a vote of 5 to 4 that it was a rabbit. Jody Powell, who voted with the majority, went ahead and released the story.

Thus the country was assured that a president who had promised Americans when he took office that he would never lie to them had once again kept his word.

But the real question that goes begging is: "Why wouldn't Mr. Carter's people believe him in the first place?"