The hierarchical nature of Chinese characters has inspired radical-based recognition, but radical segmentation from characters remains a challenge. We previously proposed a radical-based approach for on-line handwritten Chinese character recognition, which incorporates character structure knowledge into integrated radical segmentation and recognition, and performs well on characters of left-right and up-down structures (non-special structures). In this paper, we propose a statistical-classification-based method for detecting special radicals from special-structure characters. We design 19 binary classifiers for classifying candidate radicals (groups of strokes) hypothesized from the input character. Characters with special radicals detected are recognized using special-structure models, while those without special radicals are recognized using the models for non-special structures. We applied the recognition framework to 6,763 character classes, and achieved promising recognition performance in experiments.