The note is also being translated into Thai as part of the investigation, officials said.
Police Lieutenant Somyot Boonyakeow said there were no signs of a struggle in the British national's room, which did not have a balcony but had a big sealed glass window and another smaller window that could be opened.
Slym's body was identified by a Tata Motors official, said sources. An autopsy was scheduled for later today.
The executive's wife may later take the body to Britain, sources said. Boonyakeow said Slym's wife will also be interviewed.
Pornchai Suteerakune, who heads the Institute of Forensic Medicine, told reporters that Slym was killed by the fall from the 22nd floor.
