Ron Rale, Smith's attorney, said after the Los Angeles hearing the extraction "was not going to happen" within the next 24 to 40 hours as requested by photographer Larry Birkhead, who claims to be the father of Smith's 5-month-old daughter, Dannielynn.
A hearing is scheduled for Feb. 20, said Debra Opri, Birkhead's attorney.
"Everything is up in the air right now," Opri told reporters. "Everything remains as status quo."
Birkhead sought DNA samples from Smith and her daughter, still in the Bahamas, as part of his paternity suit.
Smith's remains will be preserved until the hearing, Rale said.
Howard K. Stern, Smith's longtime attorney, is listed on the birth certificate as the child's father.