  Mirror dark matter is a dissipative and self-interacting multiparticle dark
matter candidate which can explain the DAMA, CoGeNT and CRESST-II direct
detection experiments. This explanation requires photon-mirror photon kinetic
mixing of strength $\epsilon \sim 10^{-9}$. Mirror dark matter with such
kinetic mixing can potentially leave distinctive signatures on the CMB
anisotropy spectrum. We show that the most important effect of kinetic mixing
on the CMB anisotropies is the suppression of the height of the third and
higher odd peaks. If $\epsilon \stackrel{>}{\sim} 10^{-9}$ then this feature
can be observed by the PLANCK mission in the near future.
