Selection will favor males that can bias mating attempts towards more desirable females if the benefits of choosiness outweigh the costs of discrimination. Males that coexist with asexual and/or parasitically castrated females may benefit from discriminatory mating behavior because copulations with these females will not result in offspring that are related to the male. An example of a natural system in which these issues are relevant is Potamopyrgus antipodarum, a freshwater snail native to New Zealand. Sexual and asexual individuals coexist in some populations and the percentage of individuals sterilized by castrating trematodes can be very high. We addressed the possibility of male mate choice by conducting two laboratory experiments focused on determining whether male P. antipodarum housed with sexual, asexual and parasitically castrated P. antipodarum females biased copulatory effort towards sexual and/or healthy females. We found that male P. antipodarum readily copulated with asexual and castrated females, indicating that males do not avoid mating with females with whom they cannot father offspring. There was no evidence for strong male discrimination against any type of female. Potential explanations for this result include weak or no selection favoring discriminatory males, no heritable variation for male discrimination and no phenotypic indicators distinguishing sexual, asexual and healthy and sterilized females.