In static and dynamic light scattering, it has frequently been claimed that cross-polarized scattering cannot occur for single-scattering by a homogeneous spherical particle. Although this is true for both plane wave and on-axis Gaussian beam incidence, it does occur when the beam is translated off-axis incidence perpendicular to the scattering plane. An approximation to the co-polarized and cross-polarized scattering amplitudes is developed for which the sums over azimuthal modes can be evaluated analytically. This approximation provides a close fit to the exact generalized Lorenz-Mie polarization-resolved intensity for a number of off-axis locations of the incident beam.