We have used the two-degree field (2dF) multi-fiber spectrograph of the Anglo-Australian Telescope (AAT) to search for candidate members of the unusual globular cluster ω Centauri at and beyond the cluster tidal radius. Velocities with an accuracy of ~10 km s^–1 were obtained for 4105 stars selected to lie in the vicinity of the lower giant branch in the cluster color-magnitude diagram (CMD) and which cover an area on the sky of ~2.4 × 3.9 deg² centered on the cluster. Within the velocity interval 190-270 km s^–1, the cluster member candidates have a steeply declining surface density distribution consistent with the adopted cluster tidal radius of 57'. For the stars in the sample beyond the tidal radius, an analysis of line strengths from the spectra, as well as radial velocities, identifies only six stars as possible candidates for extra-tidal association with the cluster. If all six of these stars are indeed related to the cluster, then a maximum of 0.7 ± 0.2% of the total cluster mass is contained in the region between 1 and 2 tidal radii. Given this limit, we conclude that there is no compelling evidence for any significant extra-tidal population in ω Cen. The effects of tidal shocks on the outer parts of the cluster are consistent with this limit. Theories for the origin of ω Cen frequently suggest that the cluster is the former nucleus of a tidally stripped dwarf galaxy. Our results require that the stripping process must have been largely complete at early epochs, consistent with the current dynamical models of the process. The stripped former dwarf galaxy stars are therefore now widely distributed around the Galaxy.