Quoting from Sally's questioning and testimony, chief investigating officer Somyot Booyakaew said the couple, married for almost three decades, were having marital problems for quite some time.
She said they couldn't live a normal family life because of his work. Slym had to travel a lot while Sally wanted him to have more time but his duties did not allow that to happen, Somyot told reporters.
Slym, 51, fell to his death early last Sunday from a window in the suite on the 22nd floor of the riverside Shangri-la Hotel that he was sharing with Sally.
The executive came to Bangkok with his wife to attend a board meeting of the Thai subsidiary of his company.
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Somyot said Sally told police she had written the three-page letter found in their hotel room.
In the letter, Sally wrote to her husband about what she wanted from him and about her feelings, as advised by her counsellor, Somyot cited her testimony as saying.
The final conclusion on Slym's death will be announced after receiving autopsy and forensic reports, police said.
Though preliminary findings suggested Slym may have committed suicide, Somyot said his team would wait for results from the forensic police and the forensic institute.
This process might take over two months since the forensic process was getting delayed due to ongoing anti-government protests across the Thai capital, he said.