Arthur's attorney tried to argue that Birkhead and the child wouldn't return to the Bahamas for a June 8 custody hearing.
Paternity tests revealed that Birkhead was the father of 7-month-old Dannielynn. Earlier this week, the court said Birkhead and the child could go to the United States but that they were to return to the Bahamas for the June hearing.
Howard K. Stern, Smith's companion who was listed as the father on the child's birth certificate, said he would support Birkhead in any potential custody matter.
Smith died of an accidental drug overdose Feb. 8.
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