A search is presented for decays of $\mathrm {Z}$ and Higgs bosons to a ${\mathrm {J}/\psi } $ meson and a photon, with the subsequent decay of the ${\mathrm {J}/\psi } $ to $\mathrm {\mu ^+}\mathrm {\mu ^-} $ . The analysis uses data from proton-proton collisions with an integrated luminosity of 35.9 $,\text {fb}^{-1}$ at $\sqrt{s}=13,\text {TeV} $ collected with the CMS detector at the LHC. The observed limit on the $\mathrm {Z}\rightarrow {\mathrm {J}/\psi } \gamma $ decay branching fraction, assuming that the ${\mathrm {J}/\psi } $ meson is produced unpolarized, is $1.4\times 10^{-6}$ at 95% confidence level, which corresponds to a rate higher than expected in the standard model by a factor of 15. For extreme-polarization scenarios, the observed limit changes from $-13.6$ to $+8.6%$ with respect to the unpolarized scenario. The observed upper limit on the branching fraction for $\mathrm {H} \rightarrow {\mathrm {J}/\psi } \gamma $ where the ${\mathrm {J}/\psi } $ meson is assumed to be transversely polarized is $7.6\times 10^{-4}$ , a factor of 260 larger than the standard model prediction. The results for the Higgs boson are combined with previous data from proton-proton collisions at $\sqrt{s}=8,\text {TeV} $ to produce an observed upper limit on the branching fraction for $\mathrm {H} \rightarrow {\mathrm {J}/\psi } \gamma $ that is a factor of 220 larger than the standard model value.