The significance of new physics appearing in the loop-induced decays of neutral Higgs bosons into pairs of dibosons $gammagamma$ and $Zgamma$ will be discussed in the framework of the 3-3-1 models based on a recent work~cite{Okada:2016whh}, where the Higgs sector becomes effectively the same as that in the two Higgs doublet models (2HDM) after the first symmetry breaking from $SU(3)_L$ scale into the electroweak scale. For large $SU(3)_L$ scale $v_3simeq10$ TeV, dominant one-loop contributions to the two decay amplitudes arise from only the single charged Higgs boson predicted by the 2HDM, leading to that experimental constraint on the signal strength $mu^{331}_{gammagamma}$ of the Standard Model-like Higgs boson decay $hrightarrow gammagamma$ will result in a strict upper bound on the signal strength $mu^{331}_{Zgamma}$ of the decay $hrightarrow, Zgamma$. For a particular model with lower $v_3$ around 3 TeV, contributions from heavy charged gauge and Higgs bosons may have the same order, therefore may give strong destructive or constructive correlations. As a by-product, a deviation from the SM prediction $|mu^{331}_{gammagamma}-1| le 0.04$ still allows $|mu^{331}_{Zgamma}-1|$ to reach values near 0.1. We also show that there exists an $CP$-even neutral Higgs boson $h^0_3$ predicted by the 3-3-1 models, but beyond the 2HDM, has an interesting property that the branching ratio Br$(h^0_3rightarrow gammagamma)$ is very sensitive to the parameter $beta$ used to distinguish different 3-3-1 models.
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