In the preceding paper (Lacey et al., 2009), we showed that the activations evoked by visual imagery overlapped more extensively, and their magnitudes were more correlated, with those evoked during haptic shape perception of familiar, compared to unfamiliar, objects. Here we used task-specific analyses of functional and effective connectivity to provide convergent evidence. These analyses showed that the visual imagery and familiar haptic shape tasks activated similar networks, whereas the unfamiliar haptic shape task activated a different network. Multivariate Granger causality analyses of effective connectivity, in both a conventional form and one purged of zero-lag correlations, showed that the visual imagery and familiar haptic shape networks involved top-down paths from prefrontal cortex into the lateral occipital complex (LOC), whereas the unfamiliar haptic shape network was characterized by bottom-up, somatosensory inputs into the LOC. We conclude that shape representations in the LOC are flexibly accessible, either top-down or bottom-up, according to task demands, and that visual imagery is more involved in LOC activation during haptic shape perception when objects are familiar, compared to unfamiliar.