Police said the man had visited a relative in the building on Loita Street at around noon on Tuesday and, after talks, they parted only for the man to jump through the window.
“We are interrogating a few people to find out what may have triggered the suicide,” said Central police chief Paul Wanjama.
He said the middle-aged man died instantly. His body had multiple injuries and his skull was cracked open.
A student attending a college located in the building said he and his colleagues saw the man drop from the top floors as they sat their examinations.
“He was screaming as he went down. When we went outside, we found him dead. His body was really damaged,” said Pauline Njambi.
Police took the body to City Mortuary.
Elsewhere, police in Nairobi gunned down three suspected robbers and seized three pistols in two separate incidents.
Nairobi County Police Commander Japheth Koome said the three were robbing the public.
“Two of them were shot in Shauri Moyo,” said Mr Koome, adding that the other was among a gang of five that robbed a motorist at around 2am in Kibera.