"We found a window open. The window was very small so it was not possible that he would have slipped. He would have had to climb through the window to fall out because he was a big man. From my initial investigation we believe he jumped."
The police found a three-page note, written in English, which they were translating into Thai. An autopsy on Slym's body should begin on Monday.
A spokeswoman for Tata Motors, India's biggest automaker, declined to comment on the possible cause of Slym's death. A company statement on Sunday said Slym had provided leadership in a challenging market environment.
Turning the corner
Slym, a British national, was hired in 2012 to revive Tata's flagging sales and market share in India. Tata Motors is part of the Tata conglomerate.
(Read more: Singapore Air, Tata venture orders Airbus planes)
"His death comes at a time when the company seems to be close to turning the corner," said Anil Sharma, an analyst with researchers IHS Automotive. "It comes before his efforts bear fruit. We should be able to see the results in a year or two."
Tata Motors recently introduced a new petrol engine for its passenger vehicles and was planning to launch a hatchback and compact sedan this year, the first all-new Tata-branded passenger vehicles since 2010.