The STOKES Monte Carlo radiative transfer code has been extended to model the velocity dependence of the polarization of emission lines. We use STOKES to present improved modelling of the velocity-dependent polarization of broad emission lines in active galactic nuclei. We confirm that off-axis continuum emission can produce observed velocity dependencies of both the degree and position angle of polarization. The characteristic features are a dip in the percentage polarization and an S-shaped swing in the position angle of the polarization across the line profile. Some differences between our STOKES results and previous modelling of polarization due to off-axis emission are noted. In particular we find that the presence of an offset between the maximum in line flux and the dip in the percentage of polarization or the central velocity of the swing in position angle does not necessarily imply that the scattering material is moving radially. Our model is an alternative scenario to the equatorial scattering disk described by Smith et al. (2005). We discuss strategies to discriminate between both interpretations and to constrain their relative contributions to the observed velocity-resolved line and polarization.