Police were now treating his death as suspicious.
Wilson said it was unclear where Retimana went into the river.
"We're still trying to establish the exact point where he entered the river, which will be the focus of the next couple of days."
He said police would be making inquiries with the local homeless population to establish Retimana's movements before December 27, when his body was found in the river near Ann St, Awatere Ave and the Fairfield Bridge.
It was unclear how long Retimana had been homeless but Wilson said he had no family in Hamilton.
A post-mortem examination yesterday included a formal identification of the man and notification to his family.
Police appealed for information on the movements of Retimana leading up to the discovery of his body floating in the river.
People were asked to call Hamilton police on (07) 858 6200 or anonymously on 0800 555 111.