Sheila von Wiese Mack's body was found stuffed into a suitcase in the boot of a taxi in front of the St. Regis hotel Nusa Dua resort area of Bali, police said.
The 62-year-old victim was half naked, had several wounds on her head, and appeared to have put up a struggle, a doctor said.
She had been staying in the hotel with her daughter, Heather, 19, and her daughter's boyfriend, Tommy Schaefer, 21, local police chief Djoko Hari Utomo told reporters.
The next day, the couple were checking out and sent several suitcases down to a taxi, allegedly including the one that contained the victim.
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The body was discovered when the couple failed to show up at the waiting taxi, Utomo said. They were seen on CCTV leaving the hotel via a stretch of beach at the back of the property, instead of the main entrance.
"This is murder, and we will decide from our investigation whether it is premeditated or spontaneous," he said.
The victim's body was sent to the main hospital in the Balinese capital Denpasar for an autopsy. A doctor there said it had several wounds to the head, which appeared to have been inflicted with "blunt tools".
"Looking at the wounds, the victim must have fought back," said Ida Bagus Alit, adding that one of her fingers on her left hand was broken.
The US embassy in Jakarta said in a statement that it was "aware of the death of an American citizen that took place in Bali and we understand that two individuals have been arrested in connection with the case".