Complicated polarization states in the near field of Mie scattering have aroused wide interest due to their broad potential applications. In this work, we investigated polarization properties, including polarization dimension, degree of nonregularity, and transverse electric-field spin, of scattering of a partially polarized plane wave by a dielectric nanosphere based on the rigorous Mie scattering theory. It is shown that with the decrease of the correlation coefficient, the polarization dimension and degree of nonregularity generally increase. In the limit of unpolarized incident light, a nearly-perfect nonregular polarization state (PN = 0.928) appears in the near field and the spin is transverse to the radial direction everywhere. The rich structure contained by the partially polarized scattered light offers an approach to manipulating the interaction between light and nanoparticles, which may lead to novel designs of nanoantenna, optical trap and sensing.