Recently, there has been considerable interest in the dielectric properties of the cubic perovskite CaCu₃Ti₄O₁₂. The material has shown to have relatively high temperature independent dielectric permittivity over a wide temperature range from 100 K to 600 K. Below ～ 100 K the permittivity drops by almost three orders of magnitude, but is not accompanied by a structural phase transition. We studied CaCu₃Ti₄O₁₂ hoping to find signatures of local structural distortions that may explain the observe anomalies in the dielectric properties. Experiments were carried out using synchrotron radiation at several temperatures between room temperature and 10 K. Reconsideration is necessary for interpreting a huge permittivity by the local disorder model.