A search for decays of $\mathrm{Z}$ and Higgs bosons to $\mathrm{J/}\psi$ and a photon, with the subsequent decay of the $\mathrm{J/}\psi$ to $\mu^{+}\mu^{-}$, in proton-proton ($\mathrm{pp}$) collisions at a center-of-mass energy ($\sqrt{s}$) of 13~\mathrm{TeV}, is presented. The analysis uses a data sample corresponding to an integrated luminosity of 35.9~\mathrm{fb}^{-1} collected with the CMS detector at the LHC in 2016. The observed (expected) upper limit on the $\mathrm{Z}\to\mathrm{J/}\psi\ \gamma$ decay branching fraction, assuming that the $\mathrm{J/}\psi$ is unpolarized, is $1.4\ (1.6)\times10^{-6}$ at $95\%$ confidence level, which corresponds to 15 (18) times the standard model (SM) prediction. For the extreme polarization scenarios the observed (expected) limit varies from $-13.6 (-13.5)$ to $+8.6 (+8.2)\%$. The observed (expected) upper limit on the branching fraction for $\mathrm{H}\to\mathrm{J/}\psi\ \gamma$ with m_{\mathrm{H}} = 125~\mathrm{GeV} is $7.6\ (5.2)\times 10^{-4}$, 260 (170) times the SM prediction, at $95\%$ confidence level. The $\mathrm{J/}\psi$ from the Higgs decay is assumed to be completely transversely polarized. The results for the Higgs boson decay are combined with the results from $\mathrm{pp}$ collisions at \sqrt{s}=8~\mathrm{TeV} corresponding to 19.7~\mathrm{fb}^{-1} and this results in an expected (observed) upper limit on the branching fraction for $\mathrm{H}\to\mathrm{J/}\psi\ \gamma$ of 220 (160) times the SM prediction.

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