An attorney for the former boyfriend of Anna Nicole Smith has filed a second lawsuit against the reality TV star, this time alleging fraud and conspiracy, his lawyer said Thursday. 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."