EPR spectra of Cr3+ ions in single crystals of KTiOPO4 (KTP), synthesized by the flux method, have been investigated at room temperature by employing a Bruker Q-band spectrometer. From the angular dependence of the EPR pattern measured in the ab, bc, and ca planes, we have identified two Cr3+ centres, named A and B, which have been previously analysed by other investigators. In this study, we have newly identified four magnetically inequivalent Cr3+ sites for both A and B. For the four sites of both A and B, the direction cosines of the principal axes of the g as well as the second-order zero-field-splitting (ZFS) tensors are found to be given by the relationship lmn, lmn, lmn, and lmn. Using the site-rotation matrices obtained by this relationship, we calculated two sets of all spin-Hamiltonian parameters that simultaneously fitted four sites for both A and B. It is also verified that observed orientations of the principal axes for all Cr3+ sites are consistent with the crystallographic symmetry of KTP. Two possible origins of the centres A and B are proposed: each centre may be due to Cr3+ ions at crystallographically equivalent Ti sites, either Ti(1) or Ti(2), with different charge compensators, or at two different Ti sites, Ti(1) and Ti(2), without charge compensators.