Parity violation in the cosmic microwave background (CMB) radiation has been confirmed by recent Planck observation. In this paper, we extend our previous work [P. Naselsky et al. Astrophys. J. {\bf 749}, 31 (2012)] on the directional properties of CMB parity asymmetry by considering the Planck data of the CMB temperature anisotropy. We define six kinds of the directional statistics and find that they all indicate the odd-parity preference of CMB data. In addition, we find the preferred axes of all these statistics strongly correlate with the preferred axes of the CMB kinematic dipole, quadrupole, and octopole. The alignment between them is confirmed at more than $3��$ confidence level, which implies that the CMB parity asymmetry, and the anomalies of the CMB quadrupole and octopole, may have the common physical, contaminated or systematic origin. In addition, they all should be connected with the possible contamination of the residual dipole component.

18 pages, 5 figures, 5 tables