Larry Birkhead plans to ask a Nassau court to allow the retrieval of a DNA sample from Smith's 5-month-old daughter Danielynn Hope to determine her father, Birkhead's lawyer tells PEOPLE.
The child is at the center of a paternity dispute between Birkhead and Stern. Birkhead also will file a legal request that Stern relinquish custody of the child to Smith's mother, Virgie Authur.
"Larry Birkhead believes now is the time to go to the Bahamas when the whole world's magnifying glass is on the Bahamian government and the legal system," says Birkhead's attorney, Debra Opri, who is accompanying her client. "He believes he will finally get justice."
Smith died last Thursday of unknown causes in Florida. On Friday Florida police said that there was no evidence of a crime.
Police in the Bahamas questioned Stern on Monday regarding a recent alleged break-in at the home where he and Smith had been living and about the death of Smith's son Daniel, who died in September. A formal inquest into Daniel's death is scheduled to begin March 26 in the Bahamas.
Stern has not been charged with any crime.
According to a police source, Stern went to the Central Police Station in Nassau in the morning. "They called him and he came," the source says. "They should be talking to him again later on today."
Also on Monday, photos of Smith with a Bahamian official were published in a local newspaper.
The Tribune of Nassau printed two pictures of Smith in bed with immigration minister Shane Gibson, who approved her application for permanent residency in the island nation, the Associated Press reports. The two are embracing, but both are fully clothed.
The pictures were also posted on TMZ.com
According to the newspaper, the photos were shot in Smith's bedroom and obtained on Sunday from an unidentified source.
Gibson had been criticized by the political opposition for giving Smith special treatment in granting her residency last year. Before her death on Thursday, Bahamian authorities were investigating whether Smith had obtained her status legally.
At the time of Smith's death in Florida, her daughter was in the care of Gibson's mother. The infant is now being watched by Stern's family.