Federal prosecutors have opened an investigation into the mysterious slaying of a Canada Goose at an exclusive Bethesda country club. The key questioning facing the investigators is: Was the goose clubbed to death out of season?

A Washington doctor stands accused of the slaying. He has retained the attorney who represented John Dean during Watergate to defend him. And a federal investigator is working to separate the rumors about the "goose incident"-as it is referred to around Congressional Country Club-from the facts.

The date of the incident was May 3; the scene was the golf course's 17th green, and the victim was a Canada goose. On that much, everyone agrees. After that the story gets confusing.

There are those who say it was a mercy killing, that the doctor accidentally hit the goose with his approach shot, saw it was dying, and ended its suffering with his putter.

Others witnesses say the goose honked while the doctor was putting, causing him to miss the slot, and that the physician, enraged, turned on the goose and clubbed it to death.

That's were the federal government comes in, "Under the Migratory Bird Treaty Act, the secretary of the Interior has prescribed methods by which such birds can be killed," said one legal expert. A golf club is not one of them."

The law also provides that the hunting season on Canada geese.ended Jan. 26.

The accused physician, ShermanThomas, informed of the federal investigation by the U.S. attorney's office in Maryland, went to a state court Wednesday to prevent proceedings against him on another front.

Earlier in the week, Thomas won a temporary order in Montgomery County Circuit Court barring the country club's board of governors from voting on his case. The board has options ranging from no action to suspending or expelling Thomas from the club.

The incident has thrown the club into an uproar.

"Some people are supersensitive.They're reacting as if this bird was the last bald eagle," said one man at the club.

"Others think all the publicity over it is amusing, though of course it was not pleasant for the poor duck who died."

Asked whether his client, Thomas, killed the goose, attorney Charles Shaffer refused to comment.

And how is Thomas taking it all" Shaffer was asked.

"I think my client is under control and has things in perspective . . . But he has not played golf at Congressional since May 3."