The probe centers on the $1 million mansion that lawyers for Smith claimed, in an application for residency in the island chain, she had purchased, immigration director Vernon Burrows told The Associated Press.
Gaither B. Thompson, a developer from Myrtle Beach, S.C., has said that he owns the house where the 38-year-old reality star moved while pregnant with her daughter. Thompson declined to comment further.
Smith's daughter, Dannielynn Hope Marshall Stern, was born Sept. 7. Three days later, Smith's 20-year-old son, Daniel, died while visiting her in a Nassau hospital.
"Of course the only thing that would have qualified her for permanent residence was the home, so if that's no longer the case then of course we would probably ask her to show cause why it should not be revoked," Burrows said.
A Bahamian lawyer for Smith has said the former Playboy Playmate owns the home.
"I've physically seen the document that showed the property being conveyed to her," attorney Wayne Munroe told the AP. "It's not something where I'm depending on what someone told me. It was something I saw."
The official inquiry began after Burrows read media reports about Thompson's ownership claim. Burrows said his department was seeking an explanation from the law firm that handled Smith's residency application, which said she had purchased the home for $1 million and planned to spend more on renovations.
"We had no reason to question the contents of their letter," Burrows said.
Attorneys with the law firm Callenders & Co. have not returned calls seeking comment. One member of the firm, Michael Scott, withdrew as Smith's lead counsel in the Bahamas earlier this month, citing a disagreement over an undisclosed commercial transaction among other concerns.
In an e-mail to the AP on Wednesday, Smith's companion, attorney Howard K. Stern, said Smith "will be vindicated in the end."
"For the life of me, I can't understand why everybody feels the need to take shots at Anna Nicole during the most difficult time of her life with the loss of her son," Stern said.
Smith's son was buried Oct. 19. The results of official toxicology tests and a police investigation have not been publicly released.