Dawnette Knight is being held in jail in Los Angeles charged with stalking and making 24 criminal threats.
The 32-year-old student is accused of threatening 'to commit a crime which would result in death and great bodily injury'. She must raise £600,000 before being allowed bail.
In one of his most popular films, Fatal Attraction made in 1987, Douglas starred as a husband who had an affair with a woman played by Glenn Close, who stalked him and his family after he jilted her. In one scene, she famously boiled the family's pet bunny.
Knight claims she had a two-year affair with the 59-year-old star after meeting him at a party in Miami in 2002, according the U.S. magazine The National Enquirer.
Among her unsubstantiated claims, she says she stayed at the same hotel in Las Vegas as Douglas and 34-year-old Miss Zeta-Jones, while the Welsh-born actress was filming Intolerable Cruelty. She also says she was set up in an apartment in Beverly Hills by Douglas.
Last night, a spokesman for the actor called her claims 'preposterous'. He added: 'The police have the matter under control.' Miss Zeta-Jones's publicist was unavailable for comment.
The criminal threats were all allegedly made between October 3 last year and May 20. Knight, from Florida, is accused of stalking between January 2, 2003, and May 21 this year. She was arrested in West Hollywood on June 3 and appeared
in court in Los Angeles on June 10. She is due in court again next Tuesday. Although the 19-page Superior Court complaint does not name the superstar couple, the lawyer who represented Knight at the June 10 hearing, Barry Kass, confirmed Miss Zeta- Jones was the target of the threats. 'Her name was on the list of charges,' he said.
Knight's lawyer, Richard Herman, could not be contacted last night. Los Angeles police refused to comment.
In an interview with The Enquirer, Knight said: 'I met Michael in Miami in 2002. I was attending a party for the magazine Ocean Drive and Michael was there without Catherine.
'Michael came over and introduced himself. Soon we were meeting at numerous events he had to attend in different cities around the country.'
She is reported to have been thrown out of a celebrity golf tournament organised by Douglas last month after she tried to pass him a note via his bodyguards offering her phone number and asking him to call her for 'a good time'.
The magazine said Knight has no evidence to back up her story. The news comes just weeks after it emerged Miss Zeta-Jones and Douglas are having bullet-proof glass installed in the £ 2.3million mansion they are having built in her hometown of Mumbles, Swansea.
In 1999, the actress was stalked via email by a man in Chicago professing his undying love for her.
Miss Zeta-Jones is currently promoting her new film, The Terminal, costarring Tom Hanks, in which she plays a flight stewardess who falls for a man stranded in a New York airport.