Hotel surveillance footage indicated no one entered Carradine's room before he died, the policeman leading the death investigation said Saturday.
Carradine's body was reportedly flown out of Bangkok in the morning, bound for Los Angeles.
His family does not believe he committed suicide and is troubled by conflicting accounts about the circumstances of his death, Mark Geragos, an attorney for brother Keith Carradine, told CNN's Larry King late Friday.
"They want an investigation," Geragos said. "I would think that the people in Bangkok would want to support an investigation and allow the FBI to go over there and assist in the investigation so we can get the answers to the questions."
Thai police said Saturday they have not been contacted by the FBI.
Police initially said Carradine's body was found "naked, hanging in a closet," causing them to suspect he committed suicide, though no suicide note was found.
On Friday, however, police said the actor may have died from accidental suffocation or heart failure after revealing that he was found with a rope tied around his neck and penis - leading to speculation that Carradine may have engaged in a dangerous form of sex play known as auto-erotic asphyxiation.
The results of an autopsy performed Friday in Bangkok were not expected for at least three weeks, said Dr. Nanthana Sirisap, director of Chulalongkorn Hospital's Autopsy Center. Nanthana said that was normal considering the unusual circumstances of the death.
Col. Somprasong Yenthuam, who is heading the investigation, said police have interviewed all staff at the hotel where Carradine was staying and reviewed surveillance footage outside his room.
Based on that, they have found no evidence that anyone was in Carradine's room before he died which they said all but ruled out foul play.
The investigation continued Saturday, with police interviewing the crew of the film that Carradine was shooting in Bangkok.
Carradine's body was flown out of Bangkok early Saturday on a United Airlines flight bound for Los Angeles via Tokyo, according to local media and an airport official, who refused to be identified because she was not authorized to speak to the media. The US Embassy would not confirm those details.
Pornthip Rojanasunand, director of Thailand's Central Institute of Forensic Science, said the circumstances under which Carradine died suggest the 72-year-old actor may have been performing auto-erotic asphyxiation. The practice involves temporarily cutting off the supply of oxygen to the brain to heighten the effects of a sexual climax.
"In some cases it can suggest murder, too. But sometimes when the victim is naked and in bondage, it can suggest that the victim is doing it to himself," said Pornthip, considered the country's top criminal forensics expert. She did not take part in the autopsy.
"If you hang yourself by the neck, you don't need so much pressure to kill yourself," she said. "Those who get highly sexually aroused tend to forget this fact."
Carradine's body was discovered Thursday morning in his luxury suite by a chambermaid at Bangkok's Swissotel Nai Lert Park Hotel, said its general manager, Aurelio Giraudo.
Carradine flew to Thailand last week and began work on a film titled "Stretch" two days before his death. His friends and associates insisted he would not have killed himself, telling CNN's King he had a happy marriage, recently bought a new car, and had several films lined up after he finished work in Bangkok.
Carradine, a martial arts practitioner himself, was best known for the US TV series "Kung Fu," which aired from 1972-75. He played Kwai Chang Caine, an orphan who was raised by Shaolin monks and fled China after killing the emperor's nephew in retaliation for the murder of his kung fu master.
Carradine also appeared in more than 100 feature films with such directors as Martin Scorsese, Ingmar Bergman and Hal Ashby.
He returned to the top in recent years as the title character in Quentin Tarantino's two-part saga "Kill Bill." Bill, the worldly father figure of a pack of crack assassins, was a shadowy presence in 2003's "Kill Bill - Vol. 1." In that film, one of Bill's former assassins (Uma Thurman) begins a vengeful rampage against her old associates, including Bill.
