Water polarizability at a metal interface plays an essential role in electrochemistry. We devise a classical molecular dynamics approach with an efficient description of metal polarization and a novel ac field method to measure the local dielectric response of interfacial water. Water adlayers next to the metal surface exhibit higher-than-bulk in-plane and negative out-of-plane dielectric constants, the latter corresponding physically to overscreening of the applied field. If we account for the gap region at the interface, the average out-of-plane dielectric constant is quite low (ε_{⊥}≈2), in agreement with reported measurements on confined thin films.