Canine hip dysplasia (CHD) is a common and debilitating developmental condition of the canine coxofemoral (hip) joint, exhibiting a multifactorial pattern of inheritance. British Veterinary Association hip traits (BVAHTs) are nine radiographic features of hips used in several countries to ordinally score both the right and left hip of potential breeding candidates to assess their suitability for breeding. The objective of this study was to examine some aspects of the relationship between contralateral scores for each BVAHT in a cohort of 13 124 Australian-registered German Shepherd Dogs. Goodman and Kruskal gamma coefficients of 0.48–0.95 and correlation coefficients of 0.50–0.74 demonstrate that the association between right and left hip scores varies between moderate and strong for BVAHTs. Principal component analysis of scores detected a sizeable left-versus-right effect, a finding supported by symmetry and quasi-symmetry analyses which found that seven of the nine BVAHTs display significant marginal asymmetry. Dogs showing asymmetry for one BVAHT are significantly more likely to display asymmetry at other BVAHTs. When asymmetry is expressed as a binary trait (either symmetrical or asymmetrical), it displays low to moderate heritability. Estimates of genetic correlations between right and left scores are very high for all BVAHTs (>0.945), suggesting right and left scores for each BVAHT are largely determined by the same set of genes. The marginal asymmetries are therefore more likely to be of environmental and non-additive genetic origin. In breeding programmes for CHD, we recommend that scores from both hips be used to estimate breeding values, with a term for side-of-hip included in the model to account for score variation owing to asymmetry.