Using $1.06times10^8$ $psi(3686)$ events recorded in $e^{+}e^{-}$ collisions at $sqrt{s}=$ 3.686 GeV with the BESIII at the BEPCII collider, we present searches for C-parity violation in $J/psi to gammagamma$ and $ gamma phi$ decays via $psi(3686) to J/psi pi^+pi^-$. No significant signals are observed in either channel. Upper limits on the branching fractions are set to be $mathcal{B}(J/psi to gammagamma) < 2.7 times 10^{-7}$ and $mathcal{B}(J/psi to gammaphi) < 1.4 times 10^{-6}$ at the 90% confidence level. The former is one order of magnitude more stringent than the previous upper limit, and the latter represents the first limit on this decay channel.