NASSAU, Bahamas — The 20-year-old son of Anna Nicole Smith died while visiting his mother in the hospital where the reality-TV star and former Playboy playmate had given birth last week, a Bahamas police official said yesterday.

Daniel Wayne Smith died Sunday in his mother’s room at Doctors’ Hospital in Nassau, assistant commissioner of the Royal Bahamian Police Force, Reginald Ferguson, said in an interview with the Associated Press. He said an autopsy was under way. Smith arrived Saturday night in the Bahamas and apparently went directly to the hospital where he spent the night, Mr. Ferguson said.

“It would appear from our report that the mother had gotten up, saw him in the chair, and he appeared to be sound asleep,” he said. “She tried to wake him up, he was unresponsive, and she sounded the alarm.”

Medical personnel arrived and pronounced him dead at the scene, Mr. Ferguson said. Anna Nicole Smith, 38, gave birth to a healthy 6-pound, 9-ounce girl at the hospital Thursday, her Web site said.

“Anna Nicole is absolutely devastated by the loss of her son,” a statement on the site said. It said drugs or alcohol were not believed to be a factor. “Please do not make any press inquiries at this time so that Anna Nicole can grieve in peace.”

Daniel Smith was the product of Ms. Smith’s 1985 marriage to Billy Smith. The couple, who met while working together at Jim’s Krispy Fried Chicken in Mexia, Texas, divorced in 1987.