In this study, regular vine copula was used to investigate the dependence structure of electricity prices at the state level in the Australian National Electricity Market (NEM), during three periods related to the adoption and abolition of the carbon tax. In the pre-carbon period, we found evidence of tail dependence separately in the northern and southern NEM, but not across them. During the carbon period, the joint spike in the northern NEM disappeared, and the tail dependence in the southern NEM decreased. In the post-carbon period, the best dependence structure turned out to be a flexible structure of the regular vine, which exactly matches the geographical infrastructure connectedness of transmission wires. Besides, both upper and lower tail dependences were found in all adjacent states after the abolition of the carbon tax, suggesting a more integrated market regarding tail dependence. Our findings have substantial implications for risk management in the NEM, especially for those participants exposed to multiple states.