Hubert Ingraham, head of the main opposition Free National Movement, said he has learned that another person owns the waterfront mansion that Smith claimed was hers in an application for permanent residency.
"Clearly, Anna Nicole Smith is not a fit and proper person to become a permanent resident of the Bahamas," said Ingraham, a former prime minister. "Her general character and reputation don't commend her for such status."
"I expect the government of the Bahamas to make a determination in accordance with the law," he told The Associated Press in a phone interview.
Earlier this month, an attorney for Smith said concerns about her conduct contributed to his withdrawal as her counsel.
Michael Scott cited Smith's decision to exchange vows with her boyfriend and sell photographs of the informal ceremony to People magazine before burying her son.
The law says a person owning a house in the Bahamas valued at more than $500,000, having the means to live here without being employed and being of good character can be eligible for Bahamian residency.
Gaither B. Thompson of Myrtle Beach, S.C., has told The Associated Press that he owns the home where the 38-year-old celebrity moved while pregnant with her daughter, but declined further comment.
A lawyer for Smith dismissed reports that the former Playboy Playmate does not own the home.
"I've physically seen the document that showed the property being conveyed to her," Bahamian attorney Wayne Munroe told the AP. "It's not something where I'm depending on what someone told me. It was something I saw."
Immigration Minister Shane Gibson did not immediately return calls seeking comment.
Ingraham said he has been told by several people that the owner bought the home in his own name with the intention of selling it to Smith.
"If she doesn't own the house, then she would not have met the policy conditions which the government of the Bahamas has with respect to the grant of permanent residence," Ingraham said.
On Oct. 19, Smith buried her 20-year-old son Daniel, who died while visiting her in a Nassau hospital where her daughter was born on Sept. 7.
A private examiner said Daniel Smith died of an accidental lethal combination of methadone and two antidepressants. The results of official toxicology tests and a police investigation have not been publicly released.
Bahamas Chief Magistrate Roger Gomez has said authorities would soon decide whether a jury inquest into the death is necessary.
In 1985, Smith wed Bill Smith, her co-worker at a Texas restaurant, and gave birth to Daniel before divorcing two years later. And in 1994, she married Texas oil tycoon J. Howard Marshall II, when she was 26 and he was 89. He died the following year. She has since been embroiled in a legal dispute over his multimillion-dollar estate.
By Jessica Robertson