For over a decade, neuroimaging and brain stimulation studies have investigated neural mechanisms of third-party punishment, a key instrument for social norms enforcement. However, the neural dynamics underlying these mechanisms are still unclear. Previous electroencephalographic studies on third-party punishment have shown that inter-brain connectivity is linked to punishment behavior. However, no clear evidence was provided regarding whether the effect of inter-brain connectivity on third-party punishment is mediated by local neuronal states. In this study, we further investigate whether resting-state neuronal activity in the alpha frequency range can predict individual differences in third-party punishment. More specifically, we show that the global resting-state connectivity between the right dorsolateral prefrontal and right temporo-parietal regions is negatively correlated with the level of third-party punishment. Additionally, individuals with stronger local resting-state long-range temporal correlations in the right temporo-parietal cortices demonstrated a lower level of third-party punishment. Thus, our results further support the idea that global and local neuronal dynamics can contribute to individual differences in third-party punishment.