By using the crystal-field theory and third-order perturbation formula of g factor and the hyperfine structure constants A for the 3d9 electronic configuration in the planar tetragonal crystal-field as well as the quantitative relationship between the local lattice structure for the CdCl2 :Cu2 + and the electron paramagnetic resonance (EPR) spectra, the EPR spectra and local lattice structure for the CdCl2 :Cu2 + are reasonably explained. The results are well consistent with experimental findings. The core polarization constant 0.2827 was obtained. The variety of the bond length of planar tetragon is 0.013 nm. Thus, when Cu2 + is doped in CdCl2 crystal, due to the static Jahn-Teller effect, the lattice relaxation leads to the small elongation distortion in the planar tetragon.