In the construction of modern multi-storey mass timber structures, a composite floor system commonly specified by structural engineers is the timber–concrete composite (TCC) system, where a mass timber beam or mass timber panel (MTP) is connected to a concrete slab with mechanical connectors. The design of TCC floor systems has not been addressed in timber design standards due to a lack of suitable analytical models for predicting the serviceability and safety performance of these systems. Moreover, the interlayer connection properties have a large influence on the structural performance of a TCC system. These connection properties are often generated by testing. In this paper, an analytical approach for designing a TCC floor system is proposed that incorporates connection models to predict connection properties from basic connection component properties such as embedment and withdrawal strength/stiffness of the connector, thereby circumventing the need to perform connection tests. The analytical approach leads to the calculation of effective bending stiffness, forces in the connectors, and extreme stresses in concrete and timber of the TCC system, and can be used in design to evaluate allowable floor spans under specific design loads and criteria. An extensive parametric analysis was also conducted following the analytical procedure to investigate the TCC connection and system behaviour. It was observed that the screw spacing and timber thickness remain the most important parameters which significantly influence the TCC system behaviour.