Abstract We investigate the 3-3-1 model with neutral leptons, a specific extension of the 3-3-1 models {that includes} heavy neutral leptons, {which are sufficient} to accommodate the neutrino oscillation data {via} the inverse seesaw mechanism. We will point out that this model can simultaneously explain the lepton flavor violating decays of the $Z$ and Standard Model-like Higgs bosons into different charged leptons $Z,h \to e_a e_b$, {as well as} the charged lepton decays $e_b\to e_a \gamma$, in agreement with the recent experimental data. In addition, the numerical results show strong correlations among the decay rates of {the} $Z$ and $h$ {bosons} predicted by this model. {Specifically}, some of {these rates} are nearly linearly dependent on each other. {Consequently}, the decay channels can be {theoretically determined} if one of them is detected in experiments.