Noun with genitive marker in Indo-Aryan language can variously be a child of a noun, a verb or a complex predicate, thus making it an important parsing issue. In this paper, we examine genitive data of Hindi and aim to automatically determine the attachment and relational label of the same in a dependency framework. We implement two approaches: a rule based approach and a statistical approach. The rule based approach produces promising results but fails to handle certain constructions because of its greedy selection. The statistical approach overcomes this by using a single candidate approach that considers all the possible candidates for the head and chooses the most probable candidate among them. Both approaches are applied on controlled and open environment data. A Controlled environment refers to the situation when the relational labels are attested to the input data except for the genitive data; while open environment refers to cases in which the input is only POS tagged and chunked. The rule based and statistical systems produce a high accuracy of 95 % and 97 % respectively for attachment and perform considerably well for labeling in controlled environment but poorly in open environment.