President Uhuru Kenyatta has sent his condolences to Uasin Gishu Governor Jackson Mandago following the death of his brother.
John Kinyor's body was found in a building in Eldoret on Monday.
Eldoret East CID boss Ali Kingi on Wednesday said a review of CCTVs showed Kinyor, 56, slipped from stairs on the first floor and fell into an area in which a lift was to be installed.
In a statement on Wednesday, Uhuru called on law enforcement authorities to stop the rising cases of killings in the country.
"Our law enforcement agencies should move with speed to bring these senseless killings to an end. Let us deploy all resources at our disposal to ensure the safety of Kenyans across the country," he said.
It had earlier been thought that Kinyor might have been killed.
Kinyor was an employee of the Kenya Pipeline Company in Eldoret.
