The paper deals with the identification of the dative/non-dative interpretation of a non-prepositional noun (the head noun in a prepositional group) in a rule-based automatic morphological disambiguation of Czech sentences. Based on the valency considerations including syntactic functions of the complements of verbs (these functions being an object or an adverbial) and resulting in the lists of verbs having / not having object dative valency, negative and positive non-heuristic (safe) as well as heuristic rules are presented. The negative rules assign a noun a non-dative interpretation using a list of verbs that cannot tolerate a dative noun in their close vicinity, whereas the positive ones specify a given noun as being in the dative case on the basis of the verbs having an object dative valency, an object being either the only object of the verb, or its second indirect object. The paper deals only with the non-prepositional nouns which are much more difficult to disambiguate than the prepositional ones.