Pussy Riot were beaten ahead of a planned protest in Sochi
Footage shows members of the band, which became famous after performing a protest song in a church against President Vladimir Putin, being beaten.
Police questioned witnesses, but no-one was arrested.
Two band members were arrested on suspicion of theft at Sochi, but later released.
The footage shows Nadezhda Tolokonnikova and Maria Alyokhina, who both served prison sentences for their Moscow church performance, being attacked along with other band members.
A Cossack appears to spray a substance in the face of one of the band members, who were wearing ski-masks.
An officer with a whip then proceeds to attack the band members along with a man with a camera.
Other Cossacks then jump in, punching the band members and throwing them to the floor.
The group has been fiercely critical of President Putin, who has been the main driving force behind the Sochi Games.