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The dielectric properties of CuCrO2 bulk and thin films are studied by evaluating the complex dielectric function ε. In addition to the small peak near the Néel temperature TN, a secondary broad peak is found at high temperatures around Tm=450 K≫TN. As a feature of relaxor ferroelectrics, the maximum temperature Tm increases with increasing frequency. The real part of ε decreases with increasing magnetic field h and the peak at TN vanishes. The secondary peak becomes smaller and is broadened with increasing magnetic field. ε increases with increasing film thickness. Near Tm, the dielectric function offers a critical behavior expressed by an exponent γ=1.74. Using scaling arguments, critical exponents β=0.13 and δ=13.38 are deduced. The exponents depend on the film thickness. While β increases, the exponent γ is reduced with increasing film thickness. [ABSTRACT FROM AUTHOR]