Slym's body was found on a fourth-floor balcony at the Shangri-la Hotel. The Press Trust of India said Monday it appeared he plunged from a window far above, leaving an apparent suicide note behind.
Police Lt. Somyot Boonyakeow said there were no signs of a struggle in Slym's 22nd-floor room, which did not have a balcony, PTI said. He was traveling with his wife.
The Hindustan Times said the 51-year-old British national had been involved in the restructuring of the Tata Motors to help it regain its market position.
"I am deeply saddened to inform you about the untimely and tragic demise of our company's managing director, Karl Slym," Tata Chairman Cyrus Mistry said in a statement. "Karl joined us in October 2012, and was a valued colleague who was providing strong leadership at a challenging time for the Indian auto industry."
Before joining Tata, Slym had been president of General Motors India and had also worked for Toyota in England.