Searches for Higgs boson rare and invisible decays at CMS

The latest results of searches for the invisible decays of the Higgs boson (H$\rightarrow$inv) performed by the CMS Collaboration are presented. These studies represent a combination effort focusing on the data collected during the Run 1 ($\sqrt{s} = $7 and 8~TeV) and the early part of Run 2 ($\sqrt{s} = $13~TeV) period within the Large Hadron Collider (LHC). The combined result is expressed as a 95~\% Confidence Level (CL) upper limit on the branching ratio and currently stands at $\mathcal{B}$(H$\rightarrow$inv)$<$0.19 (0.15) for the observed (expected) limit. Studies of the Higgs boson decaying to a dimuon pair (H$\rightarrow\mu\mu$) are also presented. This result takes advantage of the complete dataset collected during the Run 2 period and constitutes the first evidence for the H$\rightarrow\mu\mu$ decay with the observed (expected) significance of 3.0 (2.5)~$\sigma$ and the measured signal strength, relative to the Standard Model (SM), of $\mu = $1.19$^{\text{+0.41}}_{\text{-0.39}}$(stat)$^{\text{+0.17}}_{\text{-0.16}}$(sys).