Neuronal variability in sensory cortex predicts perceptual decisions. This relationship, termed choice probability (CP), can arise from sensory variability biasing behaviour and from top-down signals reflecting behaviour. To investigate the interaction of these mechanisms during the decision-making process, we use a hierarchical network model composed of reciprocally connected sensory and integration circuits. Consistent with monkey behaviour in a fixed-duration motion discrimination task, the model integrates sensory evidence transiently, giving rise to a decaying bottom-up CP component. However, the dynamics of the hierarchical loop recruits a concurrently rising top-down component, resulting in sustained CP. We compute the CP time-course of neurons in the medial temporal area (MT) and find an early transient component and a separate late contribution reflecting decision build-up. The stability of individual CPs and the dynamics of noise correlations further support this decomposition. Our model provides a unified understanding of the circuit dynamics linking neural and behavioural variability.