A novel method for classification of abnormality in anatomical tree structures is presented. A tree is classified based on direct comparisons with other trees in a dissimilarity-based classification scheme. The pair-wise dissimilarity measure between two trees is based on a linear assignment between the branch feature vectors representing those trees. Hereby, localized information in the branches is collectively used in classification and variations in feature values across the tree are taken into account. An approximate anatomical correspondence between matched branches can be achieved by including anatomical features in the branch feature vectors. The proposed approach is applied to classify airway trees in computed tomography images of subjects with and without chronic obstructive pulmonary disease (COPD). Using the wall area percentage (WA%), a common measure of airway abnormality in COPD, as well as anatomical features to characterize each branch, an area under the receiver operating characteristic curve of 0.912 is achieved. This is significantly better than computing the average WA%.