ONE MONTH AFTER the mysterious disappearance of the coffin containing the body of the late Charlie Chaplin, police authorities and the people of this small Swiss village perched halfway up a mountain overlooking Lake Geneva are even more bewildered than they were the day Charlie's grave was found opened in the village's tiny cemetery.

Many were thought at first that the motive for stealing the solid oak casket was to extract a ransom from Chaplin's multimillion-dollar estate. Authorities, who say they have no solid leads so far, still believe that a ransom demand may be made. Since a legitimate one has not yet been received, however, a number of other theories are now popular among the baffled people living in the picturesque grape-growing region where Chaplin and his large family settled in 1954.

"I think it was fanatics," says Etienne Buenzod, the burly, rosy-cheeked village watchman, who discovered the opened grave. "If you want money, you kidnap a son or a daughter."

He was not sure from which side the fanatic came - idolizers who felt compelled to posses the lovable tramp of the silent movies or neo-Nazis who are seeking revenge for his devastating portrayal of Adolf Hitler in the film "The Great Dictator."

"Nobody knows anythings," shrugs an unemployed cigarette factory worker passing the afternoon sipping wine in the village cafe.

"It's stupid," he goes on, warming to the subject. "The culprits - fanatics - they're like pigs."

"It was either the English or his family," interjects the cafe's waitress.

"It's just my idea," she cautions, "but maybe the family moved him from the cemetery to the garden of his estate." By Swiss law, she said, a person normally cannot be buried on his own property. Police investigated but ruled out such a far-fetched scenario in this case.

A THEORY with wider currency is that British admirers who wanted Chaplin to be buried in his native England engineered the stunt. In a recent BBC interview, Frederick Sands, a family biographer and friend, boosted the proponents of this theory when he revealed that Chaplin told him some years ago that he would like to be buried in England.

To fervent Chaplin fans, Corsier's simple cemetery may not seem an appropriate resting place. Although one side (where Chaplin was buried) retains its village charm, the other end looks out over unattractive box-like cement high-rise apartment buildings and the rows of blue windows of Nestle's headquarter's in nearby Vevey.

While idle speculation abounds, police in Vevey have not ruled out ransom as the motive for a robbery that was carried out without leaving a clue.

Although there has been no serious ransom demand yet, the examining magistrate heading the investigation Jean-Daniel Tenthorey, notes that when a criminal has kidnapped a dead body "he can wait."

Tenthorey has two policemen on the case full ime, but he says they have not turned up any serious leads, although he adds "It's clear we have a few means we use but we're not able to talk about them." Nor have the police received any tips from citizens for 10 days. So for the moment, Tenthorey says with a sigh, the investigation has run out of steam. Investigations in neighboring countries and in England also have been fruitless.

IN THE FIRST couple of weeks following the robbery, several ransom demands were made, but they proved to be phony. Callers to both the authorities and to the Chaplin family's mansion were asked to give some proof, such as identifying the number on the coffin or characteristics of the body.

"But nearly always," says one investigator, "they have immediately hung up the telephones."

At the same time, many tips that often took hours to verify came from people who "think they're being helpful but are a little weak in the mind," says a police official.

Amond the crank callers was an irate man who has been arrested before in Vevey for another crime. HE roused the police out of bed at 4 a.m. to go to a place where he said they would find the coffin, but the drowsy policemen found nothing.

Meanwhile, Charlie Chaplin's grave site seems undisturbed. Marked by a simple wooden cross with his name printed in black print, it has been filled with dirt and covered with flowers.