The lawsuit was filed in the Bahamas on behalf of photographer Larry Birkhead, who claims he is the father of Smith's 6-week-old daughter, said Birkhead's attorney, Debra Opri.
Meanwhile, authorities are investigating whether Smith legally obtained permanent residency in the Bahamas, where she has been living since the birth of her daughter, the country's immigration director said Thursday.
Birkhead has been seeking a paternity test, claiming he is the father of Dannielynn Hope Marshall Stern. He filed a lawsuit in Los Angeles seeking a court order to demand Smith bring the baby to California for a test.
In the new lawsuit, Birkhead alleges Smith provided fraudulent information when applying for her daughter's birth certificate in the Bahamas. Smith identified her lawyer, Howard K. Stern, as the father. The lawsuit asks that Stern's name be deleted from the girl's birth certificate and replaced with Birkhead's.
"I am the father of Dannielynn and I think this is ... a crime," Birkhead said outside court Thursday. "I expect to be reunited with my daughter with the help of my attorneys."
A hearing in the paternity lawsuit scheduled for Thursday was delayed until early next week.
"It will be up to this government entity to pursue any criminal investigation against either Anna Nicole Smith and or Howard K. Stern," Opri said.
She said Birkhead has retained a law firm in Nassau to handle the new lawsuit, and Smith and Stern have 14 days to respond.
Smith's attorney in Los Angeles, Ronald Rale, said he has not seen the lawsuit and criticized Birkhead and his attorney for attacking his client.
"People are free to allege anything they want," Rale said. "But in the end, you better be able to back up your allegations."
The probe in the Bahamas centers on whether Smith purchased the $1 million mansion she claimed in a residency application, 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 Smith moved while pregnant with her daughter. Smith's lawyers have said the former Playboy Playmate moved to the Bahamas for privacy during her pregnancy and owns the home.
"I've physically seen the document that showed the property being conveyed to her," Bahamian attorney Wayne Munroe said. "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.
Smith's daughter was born Sept. 7. Three days later, Smith's 20-year-old son, Daniel, died while visiting her in a Nassau hospital. The results of official toxicology tests and a police investigation have not been publicly released.