Ms Altantuya Shaariibuu, 28, told her private detective, Mr Ang Chong Beng, that she was married to prominent political analyst Abdul Razak Baginda.
She told him that she wanted to track down her "husband" and would expose "everything" if Abdul Razak did not pay her US$500,000 (S$770,000).
Mr Ang, 56, said she paid him US$600 to track down Abdul Razak last September. He said she told him she married Abdul Razak, 47, a close associate of Deputy Prime Minister Najib Razak, more than two years ago in Hong Kong, although she did not show him proof of the marriage.

Murdered Mongolian model Altantuya Shaariibuu
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He said he regarded her demand for US$500,000 as a matter between husband and wife, and that if Abdul Razak "did not want her any more, he should pay".
He also said Ms Altantuya told him that if Abdul Razak did not pay up, "she will tell everything to Razak's wife, his daughter Rowena, TV3, reporters, and the whole world".
He said she also told him she had a son from another relationship in Mongolia, and the child needed medical attention. Abdul Razak yesterday denied being married to her.
He told reporters during a break in the trial that he had asked his lawyers to verify with the Hong Kong registry of marriages that no such marriage had ever taken place.
Mr Ang said Ms Altantuya called him on Oct 19, the day she went missing, to say she had received a telephone call and would be going to Abdul Razak's
house that evening.
Mr Ang, a private investigator for 22 years, kept his back to the public gallery and shielded his profile with his hand throughout his testimony. He also covered his face when confronted by press photographers outside the courtroom.
He protested when policeman Sirul Azhar's lawyer Ahmad Zaidi Zainal asked him to face the lawyers while testifying. He said press artists in the court might sketch a portrait of him for publication. That would mean he would have to stop working as a private investigator as the job required him to keep a low profile, he said.
Ms Altantuya's cousin Burmaa Oyunchimeg will take the stand today.