In this paper we explore two strategies to incorporate local morphosyntactic features in Hindi dependency parsing. These features are obtained using a shallow parser. We first explore which information provided by the shallow parser is most beneficial and show that local morphosyntactic features in the form of chunk type, head/non-head information, chunk boundary information, distance to the end of the chunk and suffix concatenation are very crucial in Hindi dependency parsing. We then investigate the best way to incorporate this information during dependency parsing. Further, we compare the results of various experiments based on various criterions and do some error analysis. All the experiments were done with two data-driven parsers, MaltParser and MSTParser, on a part of multi-layered and multi-representational Hindi Treebank which is under development. This paper is also the first attempt at complete sentence level parsing for Hindi.