Hippocampal atrophy in Alzheimer's disease (AD) is asymmetric and spatially inhomogeneous. While extensive work has been done on volume and shape analysis of atrophy of the hippocampus in AD, less attention has been given to hippocampal asymmetry specifically. Previous studies of hippocampal asymmetry are limited to global volume or shape measures, which don't localize shape asymmetry at the point level. In this paper, we propose to quantify localized shape asymmetry by optimizing point correspondences between left and right hippocampi within a subject, while simultaneously favoring a compact statistical shape model of the entire sample. To account for related variables that have impact on AD and healthy subject differences, we build linear models with other confounding factors. Our results on the OASIS3 dataset demonstrate that compared to using volumetric information, shape asymmetry reveals fine-grained, localized differences that indicate the hippocampal regions of most significant shape asymmetry in AD patients.