SEVERAL THINGS are disturbing about the case of Dr. Sherman A. Thomas, besides the actual death of the goose. For one thing, there is Dr. Thomas' story: that he wounded the goose with an approach shot to the 17th green at the Congressional County Club, and that he finished off the goose with his putter, as sort of a mercy killing. That story would be understandable, if lamentable, were it not contradicted by other golfers who say that Dr. Thomas "in a fit of rage, killed the bird after it interfered with his game." Of course the bird is game itself, which is why there is a federal law against killing it out of season. Ordinarily the difference between the accounts would be the difference between the accounts would be the difference between gooseslaughter and murder one. But an unnamed "federal source" (a source for the goose) told The Post's reporter that motives don't count. "The law does not differentiate. It says you can't kill this bird out of season, and you can't put out its misery with a putter."

That is yet another perplexing element of this case. It seems extrodinary that the federal law is specific, not to say presicent, that it has anticipated the contingency of someone using a putter as a weapon against the goose. Surely this cannot be the normal way of committing the crime.Only a goose who knew absolutely that he was cooked would sit still long enough for a killer with a putter. Then add to these the facts that the victim was a Canada goose, and yet the case will be tried in an American court, and that the lawyer whom Dr. Thomas has engaged, Charles Shaffer, is the man who represented John Dean in the Watergate scandals, and the mind begins to gaggle.

Finally, there is the matter of the "other" charge - that is, the charge that Dr. Thomas not only killed the goose, but also "unlawfully possessed" it. One hopes this merely means that the doctor carried off the goose after he did it in; but even that simple act carries a penalty of six months in jail and a $500 fine. We've come a long way from the beanstalk.

All of which proves that no matter how you slice it, the killing of a goose will get you down.