We report results of a search for the rare radiative decay B(bar sign){sup 0}{yields}D{sup *0} {gamma} . Using 9.66x10{sup 6} BB(bar sign) meson pairs collected with the CLEO detector at the Cornell Electron Storage Ring, we set an upper limit on the branching ratio for this decay of 5.0x10{sup -5} at 90% C.L. This provides evidence that the anomalous enhancement is absent in W -exchange processes and that weak radiative B decays are dominated by the short-distance b{yields}s{gamma} mechanism in the standard model. (c) 2000 The American Physical Society.