MOTIVATION: No rigorous statistical tests for detecting point-group symmetry in three-dimensional (3D) charge density maps obtained by electron microscopy (EM) and related techniques have been developed. RESULTS: We propose a method for determining the point-group symmetry of 3D charge density maps obtained by EM and related techniques. Our ab initio algorithm does not depend on atomic coordinates but utilizes the density map directly. We validate the approach for a range of publicly available single-particle cryo-EM datasets. In straightforward cases, our method enables fully automated single-particle 3D reconstruction without having to input an arbitrarily selected point-group symmetry. When pseudo-symmetry is present, our method provides statistics quantifying the degree to which the 3D density agrees with the different point-groups tested. AVAILABILITY AND IMPLEMENTATION: The software is freely available at https://github.com/hael/SIMPLE3.0.