Recent studies in monetary theory show that if buyers can use lotteries to signal the quality of bank notes, counterfeiting does not occur in a pooling equilibrium. In this paper, I investigate the robustness of this non-existence result by considering an alternative trading mechanism. Specifically, a competitive search environment is employed in which sellers post offers and buyers direct their search based on those offers. In contrast to the previous studies, buyers' ability to signal is fully eliminated in this environment. However, I find that counterfeiting does not exist if the equilibrium concept proposed by Guerrieri et al. (2010) is used. This is a refinement scheme in which sellers' out-of-equilibrium beliefs about the likelihood of meeting with different types of buyers are restricted. Moreover, a threat of counterfeiting can result in the collapse of a monetary equilibrium. An extension of the model is provided which allows the threat of counterfeiting to materialize, in that some buyers cannot observe the offers, and therefore search randomly. Counterfeit notes are produced by those buyers who randomly search.