We analyze the extent to which the sovereign Credit Default Swap (CDS) and bond markets reflect the same information on their prices in the context of the European Monetary Union. The empirical analysis is based on the theoretical equivalence relation that should exist between the CDS and bond spreads in a frictionless environment. We first test and find evidence in favour of the existence of persistent deviations between both spreads during the crisis but not before. Such deviations are found to be related to some market frictions, like counterparty risk and market-illiquidity. Finally, we find evidence suggesting that the price discovery process is state-dependent. Specifically, the levels of counterparty and global risk, funding costs, market liquidity and the volume of debt purchases by the European Central Bank in the secondary market are all found to be significant factors in determining which market leads price discovery.