Spatial correlations among proto-planetary disk orientations carry unique
information on physics of multiple star formation processes. We select five
nearby star-forming regions that comprise a number of proto-planetary disks
with spatially-resolved images with ALMA and HST, and search for the mutual
alignment of the disk axes. Specifically, we apply the Kuiper test to examine
the statistical uniformity of the position angle (PA: the angle of the major
axis of the projected disk ellipse measured counter-clockwise from the north)
distribution. The disks located in the star-forming regions, except the Lupus
clouds, do not show any signature of the alignment, supporting the random
orientation. Rotational axes of 16 disks with spectroscopic measurement of PA
in the Lupus III cloud, a sub-region of the Lupus field, however, exhibit a
weak and possible departure from the random distribution at a $2\sigma$ level,
and the inclination angles of the 16 disks are not uniform as well.
Furthermore, the mean direction of the disk PAs in the Lupus III cloud is
parallel to the direction of its filament structure, and approximately
perpendicular to the magnetic field direction. We also confirm the robustness
of the estimated PAs in the Lupus clouds by comparing the different
observations and estimators based on three different methods including sparse
modeling. The absence of the significant alignment of the disk orientation is
consistent with the turbulent origin of the disk angular momentum. Further
observations are required to confirm/falsify the possible disk alignment in the
Lupus III cloud.