  An analysis of the Higgs boson decay rates to $\gamma\gamma$ and $Z\gamma$ in
the Inert Doublet Model is presented. We study the correlation between the two
rates and perform extended analysis of the two-photon rate
($R_{\gamma\gamma}$). We study both the possibility of enhancing and
suppressing $R_{\gamma\gamma}$ and find constraints for masses of the scalar
particles (in particular the dark matter (DM) candidate and the charged scalar)
and their couplings to the Higgs boson. We also combine the resulting
constraints with those following from the WMAP measurements of the DM relic
density, obtaining stringent constraints on different dark matter scenarios.
