Using molecular dynamics computer simulation we compute gas-liquid phase coexistence curves for the Stockmayer fluid in an external electric field. We observe a field-induced shift of the critical temperature DeltaTc. The sign of DeltaTc depends on whether the potential or the surface charge density is held constant assuming that the dielectric material fills the space between capacitor plates. Our own as well as previous literature data for DeltaTc are compared to and interpreted in terms of a simple mean field theory. Despite considerable errors in the simulation results, we find consistency between the simulation results obtained by different groups including our own and the mean field description. The latter ties the sign of DeltaTc to the outside constraints via the electric field dependence of the orientation part of the mean field free energy.