The paper reports a corpus search and annotation study investigating the discourse functions of Differential Object Marking (DOM for short) in Turkish, which is manifested as optional accusative case on indefinite direct objects. Turkish DOM has been associated with specificity, presuppositionality and wide scope behavior with respect to other sentence operators. This sentence semantics has been related to different properties of discourse prominence: First to a backward discourse-linking function, where DOM-marked indefinites are indicated to have an antecedent in the discourse, without, however, there being a consensus on the type of the relation between the antecedent and the indefinite. Second, DOM in Turkish is also assumed to be related to forward direction in discourse under the general notion of being more likely to be talked about in the ensuing discourse. In order to test whether we can assign these two functions to case marking, we searched DOM tokens from a 21M corpus and annotated them with respect to categories relevant for both backward and forward discourse functions. Contrary to previous proposals and our assumptions regarding backward and forward linking, we did not observe any discourse function in either direction in our data set. We provide some arguments for why Turkish case marking does not show the discourse functions that are demonstrated for other languages.