Huntington's disease (HD) is a progressive inherited brain disorder that affects cognition, personality and physical abilities. Advanced statistical shape analysis pipelines have shown that region-specific shape abnormalities of the putamen and thalamus begin earlier than clinical onset ('premanifest' period), but the order and pattern of different subregions' abnormalities of those two structures are still unclear. In this paper, we applied a multivariate linear mixed-effects model, in combination with a novel shape diffeomorphometry technique, to identify the changepoints at which the shape morphometry abnormalities of different putamen and thalamus sub-regions start. Our experimental results revealed that the putamen was affected severely by HD whereas the thalamus was affected in a milder way. The putaminal subregion connected to the executive cortex and the thalamic subregion connected to the prefrontal cortex were found to be affected the earliest by HD. This study contributes to a better understanding of the temporal ordering of the putaminal and thalamic abnormalities of different functionally-distinct subregions.