The way artist Robert N. Williams tells it, this is a story about a chance encounter with a stranger on a train that turned into something of a nightmare. According to Williams, that stranger took advantage of the December encounter by strolling into the artist's Rockville shop last week and robbing him at gunpoint.

The loot? A statue of a nude woman that Williams says is "worth its weight in gold," which is exactly what Williams said it was made of. He said the 568-gram, 18-carat statue has a current market value of $47,500.

Montgomery County police at first were so suspicious of the story that they asked Williams to take a lie-detector test. According to police, he did so and passed.

Now, in a strange tale that mixes the best and shadiest elements of a Dashiell Hammett mystery, the plot has thickened to a point where the FBI is poised to enter the case. And for the moment, no one except Williams seems entirely sure about what really happened.

"I feel I've been mentally raped," the artist said. "It seems ironic the police would see me as the prime suspect . . . By now that guy's probably melted the statue down."

The police, meanwhile, have declined to comment, except to say they have solid leads and expect an arrest soon.

"It's an ongoing investigation," said detective Mike Turner, "so there's not a whole lot I want to tell you."

First, the facts: Williams' shop, Advanced Design Concepts, is located at 11600 Nebel St. A jeweler by trade, Williams has been spending more time recently designing a solid gold statue he calls the "Sunbather." Last month he cast a model of the 7 1/2 inch by 3 1/2 inch statue, which depicts a nude woman reclining, her leg propped up and a hand on her forehead.

Williams said he planned to enter the fully insured statue in a New York art contest because of its uniqueness. He said he hoped to donate the statue to the Smithsonian Institution, then concentrate on casting a limited edition of "10 or 12" of them to be sold to wealthy art collectors.

To that end, he said, he traveled to New York City on Dec. 15 to have dinner with an associate and to plan a party at the associate's home with "an exclusive group of people--actors, financial wizards."

Late that night, returning to Washington on an Amtrak train, he said he struck up a conversation with a "well-mannered, well-dressed" man with a beige suit bag beside him. The man said his name was "T.J." and that he was a salesman, Williams recalled. Upon learning that Williams was a jeweler and an artist, the man said he would like to visit Williams and have a necklace designed and made for him.

Williams said he gave the man his business card, and a couple of weeks later the man telephoned, said he had won $4,000 in a poker game and asked to visit Williams' shop.

On Jan. 5, the stranger appeared. Williams said he recognized the voice over an outside intercom and pressed a buzzer to admit him into the office. After the man had perused a number of designs and pieces of jewelry, Williams said the man suddenly pulled out a small-caliber gun.

"He said, 'Remember that poker game?' " Williams said. " ' . . . well, the truth is I lost $15,000 and there's some men out to kill me. I'm sorry I have to do this.' "

Debbie Simonsen, 19, who assists Williams at the shop, was present during the incident. "He was nervous, almost like he was about to cry," she said of the bandit, whom she described as about 5-feet-11, 165 pounds, and wearing a gray three-piece suit.

Simonsen said the man tied her hands and Williams' behind their backs with a length of gold-colored cord he pulled from his coat and proceeded to pocket jewelry and watches. Then, she said, the man took the necklaces and pendants Williams had shown him.

"Finally," Williams recalled, "I said, 'Take anything you want, but leave the statue alone,' " at which point the man took the statue as well, and fled.

Williams, who freed his hands "within seconds," said he spent the next few days answering police questions. "It's just they found the whole thing so implausible," he said.

He took the polygraph and said detective Turner called him two days ago to tell him he passed it. "He said he was satisfied and that he would call in the FBI because of the possibility that the statue has been taken across state lines," Williams said.

"It's insured so I'm not too worried about that," he went on. "It's just the effort that's involved. It takes me two-and-a-half months to make one of those things."