Carradine's naked body was discovered last Thursday morning in his luxury suite at Bangkok's Swissotel Nai Lert Park Hotel. Police initially suspected his death was a suicide, but have since said it may have been accidental suffocation or heart failure after revealing he was found with a rope tied around his wrist, neck and genitals.
The circumstances suggested he might has died as a result of a dangerous sex game, Pornthip Rojanasunand, a prominent Thai forensic pathologist, said last week.
With the uncertainty and conflicting information surrounding the death, Carradine's family in the U.S. went to the FBI last Friday asking for its help investigating the case.
"If the FBI wants to get involved, we will do our best to cooperate," Thai police Maj. Gen. Amnuay Nimmano told reporters, adding that it would have to be in an observer role as mandated by Thai law. "We have nothing to hide."
Sirisak Tiyapan, director-general for International Affairs of Thailand's Attorney General's Office - which would handle any cooperation with U.S. law enforcement agencies - said his agency had not yet received a request from the FBI to assist in the Carradine case.
U.S. Embassy Spokesman Michael Turner said he couldn't comment on the investigation but did acknowledge that FBI agents attached to the embassy were talking informally about the case with their Thai police counterparts.
FBI spokeswoman Laura Eimiller said earlier that the agency generally only gets involved in death investigations overseas if a crime is suspected.
After numerous leaks about the crime scene and cause of death, Maj. Gen. Amnuay at Monday's press conference sought to quash further speculation. He refused to comment on the condition Carradine's body was found in or the reports that he died from the dangerous form of sex play known as auto-erotic asphyxiation.
"The previous conclusions on the cause of death were made by people who know nothing about the case," Amnuay told reporters, adding that he had to protect the privacy of Carradine's family.
The actor's family has said they hoped his body would arrive in Los Angeles by Monday, said their attorney, Mark Geragos, but he did not give specifics.
The family will also seek an independent autopsy by famed forensic pathologist Dr. Michael Baden to determine whether another person could have been involved in causing Carradine's death, Geragos said. Results of an autopsy performed Friday in Bangkok were not expected for at least three weeks.
Carradine flew to Thailand at the end of May and began work on a film titled "Stretch" two days before his death. His friends and associates told CNN's Larry King he had a happy marriage, had recently bought a new car, and had several films lined up after he finished work in Bangkok.
A martial arts practitioner himself, Carradine was best known for the U.S. 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 for the American West 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."
Funeral arrangements have not been announced.
By Michael Casey