Studies of rare decays play an important role in the search for physics beyond the standard model. Recent results from the CMS experiment on the decays of B and $\tau$ particles to final states containing muons, based on 8 and 13 TeV data, are presented. In addition, the perspectives for the measurements of the $B^0_s \to \mu^+\mu^−$ and $B^0 \to \mu^+\mu^−$ branching fractions and $B^0_s \to \mu^+\mu^−$ effective lifetime at the High-Luminosity LHC are reported, together with the projections for the sensitivity of the $P′_5$ parameter in the $B^0 \to K^{0∗}\mu^+\mu^−$ angular analysis.