An extensive empirical literature documents a generally negative correlation, named the “leverage effect,” between asset returns and changes of volatility. It is more challenging to establish such a return-volatility relationship for jumps in high-frequency data. We propose new nonparametric methods to assess and test for a discontinuous leverage effect — i.e. a relation between contemporaneous jumps in prices and volatility — in high-frequency data with market microstructure noise. We present local tests and estimators for price jumps and volatility jumps. Five years of transaction data from 320 NASDAQ firms display no negative relation between price and volatility cojumps. We show, however, that there is a strong relation between price-volatility cojumps if one conditions on the sign of price jumps and whether the price jumps are market-wide or idiosyncratic.