According to the social intelligence hypothesis, understanding the challenges faced by social animals is key to understanding the evolution of cognition. In structured social groups, recognising the relationships of others is often important for predicting the outcomes of interactions. Third-party relationship recognition has been widely investigated in primates, but studies of other species are limited. Furthermore, few studies test for third-party relationship recognition in the wild, where cognitive abilities are deployed in response to natural socio-ecological pressures. Here, we used playback experiments to investigate whether wild jackdaws (Corvus monedula) track changes in their own relationships and the relationships of others. Females were presented with ‘infidelity simulations’: playbacks of their male partner copulating with a neighbouring female, and their male neighbour copulating with another female, against a congruent control. Our results showed substantial inter-individual variation in responses, but females did not respond more strongly to infidelity playbacks, indicating that jackdaws may not attend and/or respond to relationship information in this experimental context. Our results highlight the need for further study of relationship recognition and other cognitive traits that facilitate group-living in the wild, particularly in non-primates and in a wider range of social systems.