This paper analyses Delta CoVaR proposed by Adrian and Brunnermeier (2008) as a tool for identifying/ranking systemically important institutions and assessing interconnectedness. We develop a test of significance of Delta CoVaR that allows determining whether or not a financial institution can be classified as being systemically important on the basis of the estimated systemic risk contribution, as well as a test of dominance aimed at testing whether or not, according to Delta CoVaR, one financial institution is more systemically important than another. We provide two applications on a sample of 26 large European banks to show the importance of statistical testing when using Delta CoVaR, and more generally also other market-based systemic risk measures, in this context.