Thermally stimulated depolarization current (TSDC) measurements of CaF₂:Cu⁺ samples show three different dipolar relaxation bands, with temperature peaks at 52, 144 and 187 K. The two higher temperature bands are more intense and reveal the presence of Cu⁺ in probably two different lattice sites. The band at 144 K suggests it is related to the Cu⁺ off-center effect, observed through an optical absorption at 328 nm, and it is likely temperature independent. To this Cu⁺ off-center effect it is also associated an impurity-vacancy defect, that result from needed charge compensation in CaF₂. The observed TSDC band at 187 K is attributed to Cu_i⁺—F_i^- pair, both ions in interstitial positions. The weakest TSDC at 52 K is assumed to be from a low un-intentional Mn²⁺ doping, sitting in an off-center substitutional position. It is proposed a model to explain the several positions available for the substitutional Cu⁺ that response for the TSDC result.