We show that Combinatory Categorial Grammar (CCG) supertags can improve Telugu dependency parsing. In this process, we first extract a CCG lexicon from the dependency treebank. Using both the CCG lexicon and the dependency treebank, we create a CCG treebank using a chart parser. Exploring different morphological features of Telugu, we develop a supertagger using maximum entropy models. We provide CCG supertags as features to the Telugu dependency parser (MST parser). We get an improvement of 1.8% in the unlabelled attachment score and 2.2% in the labelled attachment score. Our results show that CCG supertags improve the MST parser, especially on verbal arguments for which it has weak rates of recovery.