The search for the charged lepton flavor violating decay $\tau \rightarrow 3\mu$ has been performed at the CMS experiment at the LHC, using data collected in 2016 during proton-proton collisions. The data sample corresponds to an integrated luminosity of 33.2 $fb^{-1}$, recorded at a center-of-mass energy of 13 TeV. The results obtained by exploiting tau leptons produced in decays of heavy flavor $B$ and $D$ mesons and from $W$ bosons have been combined and they are presented in this contribution. No significant excess was observed and an upper limit on the branching fraction of $\mathcal{B}(\tau \rightarrow 3\mu)$ of $8.0 \times 10^{-8}$ at 90% confidence level was set.