Several experimental studies in the literature have shown that even when performing purely kinesthetic tasks, such as reaching for a kinesthetically felt target with a hidden hand, the brain reconstructs a visual representation of the movement. In our previous studies, however, we did not observe any role of a visual representation of the movement in a purely kinesthetic task. This apparent contradiction could be related to a fundamental difference between the studied tasks. In our study subjects used the same hand to both feel the target and to perform the movement, whereas in most other studies, pointing to a kinesthetic target consisted of pointing with one hand to the finger of the other, or to some other body part. We hypothesize, therefore, that it is the necessity of performing inter-limb transformations that induces a visual representation of purely kinesthetic tasks. To test this hypothesis we asked subjects to perform the same purely kinesthetic task in two conditions: INTRA and INTER. In the former they used the right hand to both perceive the target and to reproduce its orientation. In the latter, subjects perceived the target with the left hand and responded with the right. To quantify the use of a visual representation of the movement we measured deviations induced by an imperceptible conflict that was generated between visual and kinesthetic reference frames. Our hypothesis was confirmed by the observed deviations of responses due to the conflict in the INTER, but not in the INTRA, condition. To reconcile these observations with recent theories of sensori-motor integration based on maximum likelihood estimation, we propose here a new model formulation that explicitly considers the effects of covariance between sensory signals that are directly available and internal representations that are 'reconstructed' from those inputs through sensori-motor transformations.