The use of cross-polarized antennas for multiple-input multiple-output (MIMO) systems is receiving attention as they are able to double the number of antenna for half antenna spacing needs. This paper presents the channel correlation property of the 3rd Generation Partner Project (3GPP)/3GPP2 spatial channel model (SCM) with the polarization propagation. The statistical average of the per path polarization correlation given random cross-polarization discrimination (XPD) with co-located ideal tilted dipole antennas is derived. The impact on the random behavior of the polarization correlation due to the slant offset angle, the per path angular spread (AS), and the random XPD is analyzed. The simulation results show that the variation of polarization correlation caused by the random XPD is maximized with a 58° slant offset angle under the assumptions of all predefined scenarios in SCM. The per path AS has minor impact on the statistics of the polarization correlations. The randomness of polarization correlation is negligible for an XPD with small standard deviation.