In this paper, we analyzed the effect of ocular dominance on touch positions when users touched a three-dimensional (3D) object on a two-dimensional (2D) touch panel while watching a 3D display. We performed a psychophysical experiment where eight subjects (four right-eye-dominant and four left-eye-dominant) participated. When touching 3D objects with uncrossed disparities, touch positions were mainly influenced by ocular dominance and depth of the 3D image $(P < 10^{-189})$. For crossed disparities, touch positions were mainly influenced by ocular dominance $(P < 10^{-18})$. However, the depth of the 3D image had no significant effect on touch positions $(P = 0.783)$. Our findings can help to design more accurate and comfortable interfaces for 3D systems with touch feedback.