The movements of the different speech articulators are known to be correlated to various degrees. Thus, it is important to investigate whether the estimated articulator trajectories in the acoustic‐to‐articulatory inversion preserve similar correlation patterns. In this work, the inter‐articulator correlation in the context of the articulatory inversion is investigated using the generalized smoothness criterion (GSC). In GSC, the articulator‐specific smoothness constraints are considered during articulatory inversion. GSC estimates each articulator separately without explicitly using any correlation information between the articulators and, therefore, a methodology is proposed to explicitly impose the inter‐articulator correlation for the acoustic‐to‐articulatory inversion using GSC. Based on the theoretical and experimental investigations, it is found that the GSC inherently preserves the inter‐articulator correlation to a certain extent and, hence, there is no significant benefit by explicitly using the inter‐articulator correlation information during the articulatory inversion using GSC.