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 → e_a e_b, as well as the charged lepton decays e_b → e_a γ, 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.