Based on the studies of the electron paramagnetic resonance parameters for two types of the Cu centers in Cd(HCOO) ·2H O by using the high-order perturbation formulas for a 3d ion in a rhombically elongated octahedron, local structure of the doped copper ion is determined. Research suggests that the impurity Cu replaces the host Cd and undergoes the local rhombic elongation distortion, characterized by the axial elongation ratios of 4.1%, and 3.8% along the z-axis and the planar bond length variation ratios of 3.8%, and 3.1% along the x-axis and y-axis, for Cu Centers, I and II, respectively. The above slightly different axial elongation ratios and planar bond length variation ratios may suitably account for the slightly dissimilar axial g anisotropies Δg (≈0.351 and 0.339) and perpendicular g anisotropies δg (≈0.028 and 0.022) of the two centers, respectively.