Observations of Titan's whole disk polarization at 2460 and 7500 ¿ are presented and analyzed in terms of model scattering atmospheres. If the Titan aerosols are spherical or nearly spherical, no single combination of refractive index and size distribution is able to fit data at both wavelengths. However, a vertically homogeneous distribution suggested by Tomasko and Smith (1980), characterized by a size gradient with altitude, fits the data at 2640 ¿ moderately well but must be modified at intermediate and large optial depths to fit the 7500-¿ data. Results for synthetic phase functions indicate that the single scattering polariztion must be 70% or larger in the UV and 78% or larger in the near-IR at 90¿ phase angle, depending on the phase function. If the correct phase function is similar to that for 0.5-&mgr;m-radius spheres, the UV single-scattered polarization must be 84% and the near-IR single-scattered polarization must over 90%. Such large polarizations are impossible for 0.5-&mgr;m-radius spheres but may be possible for nonspherical particles with effective radii near 0.5 &mgr;m, although the existence of nonspherical particles with the scattering properties required by these and other observations has not been demonstrated.