It is well established that building construction using volumetric modules has numerous advantages over traditional construction; however, achieving simple, yet high-performance inter-module connectivity, poses unique challenges in relation to the structural performance, fabrication, and overall construction. In an attempt to address these challenges, a three-piece boltless inter-module connection was developed for safe and instant vertical and horizontal connectivity of modules in multi-storey steel buildings. The key focus of this paper is to present the local behaviour of this connection and assess its performance on the global structural behaviour in mid- to high-rise modular buildings. The local behavioural characteristics are established through finite element models, and simplified analytical equations are also derived to estimate the stiffness and strength limits. A global performance study is also performed to compare the overall structural performance of different inter-module connection types in a case study 20-storey modular building. The structural performance indicators including the inter-storey drifts and the relevant demand-to-capacity ratios for the connection indicate that the proposed connection satisfactorily meets performance expectations, i.e. the drifts at serviceability were within 0.2% and the ultimate limit state connection demands were well within the targeted elastic limits.