  The observation of the $\mathrm{Z}$ boson rare decay to a $\psi$ meson and
two oppositely charged same-flavour leptons, $\ell^+ \ell^-$, where $\psi$
represents the sum of $\mathrm{J}/\psi$ and
$\psi(\mathrm{2S})\to\mathrm{J}/\psi\, X$, and $\ell=\mu,\mathrm{e}$, is
presented. The data sample used corresponds to an integrated luminosity of
$35.9\,\mathrm{fb}^{-1}$ of proton-proton collisions at a center-of-mass energy
of $13\,\mathrm{TeV}$ accumulated by the CMS experiment at the LHC. The signal
is observed with a significance in excess of 5 standard deviations. Removing
contributions from $\psi(\mathrm{2S})$ decays to $\mathrm{J}/\psi$, the signal
is interpreted as being entirely from
$\mathrm{Z}\to\mathrm{J}/\psi\,\ell^+\ell^-$, with its fiducial branching
fraction relative to that of the decay $\mathrm{Z}\to\mu^+\mu^-\mu^+\mu^-$
measured to be
$$\frac{\mathcal{B}(\mathrm{Z}\to\mathrm{J}/\psi\,\ell^+\ell^-)}{\mathcal{B}(\mathrm{Z}\to\mu^+\mu^-\mu^+\mu^-)}=0.70\pm
0.18\, \mathrm{(stat)} \pm 0.05\, \mathrm{(syst)}.$$ This result is obtained
with the assumption of no $\mathrm{J}/\psi$ polarisation, where extreme
polarisation scenarios can create $-24\%$ to $+22\%$ variations.
