Spatial correlations among protoplanetary disk orientations carry unique information on physics of multiple-star formation processes. We select five nearby star-forming regions that comprise a number of protoplanetary disks with spatially resolved images with ALMA and Hubble Space Telescope, and we 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 counterclockwise 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 subregion of the Lupus field, however, exhibit a weak and possible departure from the random distribution at a 2σ 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.