This paper investigates the asymmetric conditional dependence between Shanghai and Hong Kong stock index returns, to assess the impact of the recent financial recession on Chinese equity markets using the Copula approach. We first propose methods for optimal model selection when constructing the conditional margins. The joint conditional distribution is then modelled by the time-varying copula, where the generalised autoregressive score (GAS) model of Creal et al. (2013) is used to capture the evolution of the copula parameters. Upper and lower parts of the bivariate tail are estimated separately in order to capture the asymmetric property. We find the conditional dependence between the two markets is strongly time-varying. While the correlation decreased before the crisis, it increased significantly prior to 2008, pointing to the existence of contagion between the two markets. Moreover, we find a slightly stronger bivariate upper tail, suggesting the conditional dependence of stock returns is more significantly influenced by positive shocks in China. This finding is further confirmed by a test for asymmetry which shows that the difference between upper and lower joint tails is significant.