We present the results of a search for the standard model Higgs boson production in the rare $\mu^+\mu^-$ decay channel in proton-proton collisions at \mbox{$\sqrt{s}=7$ and 8~TeV}. The data samples, recorded by the CMS experiment at the LHC, correspond to integrated luminosities of $5.0\pm0.1$~fb$^{-1}$ at 7 TeV and of $19.7\pm0.5$~fb$^{-1}$ at 8 TeV. To enhance the Higgs signal over the dominant Drell-Yan background, the events are categorized by topologies corresponding to different production processes. Upper limits on the production cross section at the 95\% confidence level are reported for Higgs boson masses in the range from 120 to 150~\GeVcc. At the Higgs boson mass of 125~\GeVcc the observed (expected) 95\% C.L. upper limit on the production rate is found to be 7.4 ($5.1^{+2.3}_{-1.5}$) times the standard model prediction. %For a dimuon mass at 149~\GeVcc, a broad excess corresponding to a local significance of 2.8~\sigma %and 1.6~\sigma after taking into account the look-elsewhere effect is observed. Results of the first search for the Higgs boson production in the rare decay $\mathrm{e}^+\mathrm{e}^-$ is also reported.

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