This article develops statistical tools for testing conditional independence among the jump components of the daily quadratic variation, which we estimate using intraday data. To avoid sequential bias distortion, we do not pretest for the presence of jumps. If the null is true, our test statistic based on daily integrated jumps weakly converges to a Gaussian random variable if both assets have jumps. If instead at least one asset has no jumps, then the statistic approaches zero in probability. We show how to compute asymptotically valid bootstrap-based critical values that result in a consistent test with asymptotic size equal to or smaller than the nominal size. Empirically, we study jump linkages between US futures and equity index markets. We find not only strong evidence of jump cross-excitation between the SPDR exchange-traded fund and E-mini futures on the S&P 500 index, but also that integrated jumps in the E-mini futures during the overnight period carry relevant information. for this article are available as an online supplement.