The lawyer for photographer Larry Birkhead traveled from Los Angeles to take a deposition from Smith in the Bahamas, where the former Playboy playmate moved while she was pregnant and declared her current companion Howard K. Stern as the child's father.
Birkhead filed a lawsuit in Los Angeles seeking a court order to demand Smith bring the baby to California for a paternity test. Her attorneys have argued the court does not have appropriate jurisdiction, but Birkhead lawyer Debra Opri said she would use Smith's nonappearance Monday to argue for dismissal of that challenge.
"We're letting her know if she wants to make it this way, we're not going to make it easy for her," Opri said in a phone interview from Nassau. "This is a tragedy of a natural father, Larry Birkhead, who is being deprived of the bonding process of a father and his daughter."
A Bahamian attorney for Smith said he believed Opri needs to work through local courts to demand a test from his client, who has obtained permanent residency in the islands.
"If anyone is to be inconvenienced, let him be inconvenienced and bring this action here," Wayne Munroe said of Birkhead.
Munroe said Smith stood by her decision not to voluntarily submit her daughter for testing.
"If this young woman thinks advertising will sway my client, she is rudely mistaken," he said, referring to Opri.
In a statement Monday to syndicated TV show "Extra," Stern said the meeting to take depositions was "nothing more than a publicity stunt."
Smith may be facing eviction from the New Providence, Bahamas, home where she is currently living. A real estate developer from Myrtle Beach, S.C., tells People magazine that he owns the property.
G. Ben Thompson said he purchased the million-dollar home in August as a favor to the reality star, but he added that she thinks it's a gift. Thompson said that if Smith does not move out he will formally evict her — even though he doesn't want to embarrass or humiliate her.
A lawyer for Smith would not confirm or deny Thompson's claims. It's unclear whether or not the eviction would affect her residency status in the Bahamas.
A hearing in the paternity case has been scheduled for Thursday at Los Angeles Superior Court. If Birkhead is confirmed to be the father, he could receive visitation or custody rights and possibly a large amount of child support.
The baby girl, Dannielynn Hope Marshall Stern, was born on Sept. 7, three days before Smith's 20-year-old son Daniel died while visiting his mother and half-sister in the hospital.
A private examiner has said Daniel died from a lethal combination of methadone and two antidepressants. Local officials were expected to announce this week whether they would call a jury inquest into the death.