Zimin, an investigative reporter who worked with the NTV network, was found dead on 26 February in his apartment in the north of Moscow.
Prosecutors said he died after being severely beaten by unknown assailants. They said his death was not connected to his reporting work.
Before moving to Moscow in 2000, Zimin headed NTV's Far East bureau. He also worked for the TV6 and TVS television channels.
He survived a previous attack last April, when he was violently beaten outside the entrance to his apartment building.
The New York-based Committee to Protect Journalists has listed Russia among the world's 10 most-hazardous countries for reporters.
(Interfax, RIA Novosti, AP)
