Animals exchanges are considered the most effective route of between-farm infectious disease transmission. However, despite being often overlooked, the infection spread due to contaminated equipment, vehicles, or personnel proved to be important for several livestock epidemics. This study investigated the role of indirect contacts in a potential infection spread in the dairy farm network of the Province of Parma (Northern Italy). We built between-farm contact networks using data on cattle exchange (direct contacts), and on-farm visits by veterinarians (indirect contacts). We compared the features of the contact structures by using measures on static and temporal networks. We assessed the disease spreading potential of the direct and indirect network structures in the farm system by using data on the infection state of farms by paratuberculosis. Direct and indirect networks showed non-trivial differences with respect to connectivity, contact distribution, and super-spreaders identification. Furthermore, our analyses on paratuberculosis data suggested that the contributions of direct and indirect contacts on diseases spread are apparent at different spatial scales. Our results highlighted the potential role of indirect contacts in between-farm disease spread and underlined the need for a deeper understanding of these contacts to develop better strategies for prevention of livestock epidemics.