Forensic assessments of postmortem decomposition often rely on external, whole-body signs, yet structural changes within organs remain largely unquantified. Using whole-body computed tomography scans of 59 decedents from the New Mexico Decedent Image Database, we conduct an organ-level statistical shape analysis of decomposing brains and kidneys, representing each organ as a three-dimensional point cloud of its outer surface and internal cavity boundaries. Decomposition creates voids, fragmentation, and structural heterogeneity, complicating point correspondence. Registration-based principal component analysis and principal nested cones yield interpretable orderings for brains only. We therefore construct a registration-free pipeline using persistent homology and a fusion of complementary topological distances selected through simulations of cavity formation and growth. Clustering identifies broad patterns of internal decay, and seriation produces organ-specific decomposition atlases. The brain atlas combines geometric and topological rankings; the kidney atlas uses topology alone. Rank agreement is higher between paired kidneys (Kendall's $τ= 0.59$) than between brains and kidneys ($τ= 0.34$ to $0.39$), indicating asynchronous decompositions within a body. Whole-body stages agree more closely with brain than with kidney rankings. These findings support quantitative forensic taphonomy by complementing whole-body staging with organ-level, interior-based measurements. We release the organ point clouds and analysis code to support research on organ decomposition and shape analysis without reliable correspondence.

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