The ionization of a beam of H2 Rydberg molecules in collision with a metal surface (evaporated Au or Al) is studied. The Rydberg states are excited in an ultraviolet-vacuum ultraviolet double-resonant process and are state selected with a core rotational quantum number N+=0 or 2 and principal quantum numbers n=17-22 (N+=2) or n=41-45 (N+=0). It is found that the N+=0 states behave in a very similar manner to previous studies with atomic xenon Rydberg states, the distance of ionization from the surface scaling with n2. The N+=2 states, however, undergo a process of surface-induced rotational autoionization in which the core rotational energy transfers to the Rydberg electron. In this case the ionization distance scales approximately with nu0(2), the effective principal quantum number with respect to the adiabatic threshold. This process illustrates the close similarity between field ionization in the gas phase and the surface ionization process which is induced by the field due to image charges in the metal surface. The surface ionization rate is enhanced at certain specific values of the field, which is applied in the time interval between excitation and surface interaction. It is proposed here that these fields correspond to level crossings between the N+=0 and N+=2 Stark manifolds. The population of individual states of the N+=2, n=18 Stark manifold in the presence of a field shows that the surface-induced rotational autoionization is more facile for the blueshifted states, whose wave function is oriented away from the surface, than for the redshifted states. The observed processes appear to show little dependence on the chemical nature of the metallic surface, but a significant change occurs when the surface roughness becomes comparable to the Rydberg orbit dimensions.