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We present a statistical characterization of circumstellar disk orientations toward 12 protostellar multiple systems in the Perseus molecular cloud using the Atacama Large Millimeter/submillimeter Array at Band 6 (1.3 mm) with a resolution of ∼25 mas (∼8 au). This exquisite resolution enabled us to resolve the compact inner-disk structures surrounding the components of each multiple system and to determine the projected 3D orientation of the disks (position angle and inclination) to high precision. We performed a statistical analysis on the relative alignment of disk pairs to determine whether the disks are preferentially aligned or randomly distributed. We considered three subsamples of the observations selected by the companion separationsa< 100 au,a> 500 au, anda< 10,000 au. We found for the compact (<100 au) subsample, the distribution of orientation angles is best described by an underlying distribution of preferentially aligned sources (within 30°) but does not rule out distributions with 40% misaligned sources. The wide companion (>500 au) subsample appears to be consistent with a distribution of 40%–80% preferentially aligned sources. Similarly, the full sample of systems with companions (a< 10,000 au) is most consistent with a fractional ratio of at most 80% preferentially aligned sources and rules out purely randomly aligned distributions. Thus, our results imply the compact sources (<100 au) and the wide companions (>500 au) are statistically different.