Dimensionality analysis of magnetotelluric data is a common procedure for inferring the main properties of the geoelectric structures of the subsurface such as the strike direction or the presence of superficial distorting bodies, and enables the most appropriate modeling approach (1D, 2D or 3D) to be determined. Most of the methods currently used assume that the electrical conductivity of individual parts of a structure is isotropic, although some traces of anisotropy in data responses can be recognized. In this paper we investigate the imprints of anisotropic media responses in dimensionality analysis using rotational invariants of the magnetotelluric tensor. We show results for responses generated from 2D synthetic anisotropic models and for field data that have been interpreted as showing the effects of electrical anisotropy in parts of the subsurface structure. As a result of this study we extend the WAL dimensionality criteria to include extra conditions that allow anisotropic media to be distinguished from 2D isotropic ones. The new conditions require the analysis of the strike directions obtained and take into account the overall behavior of different sites in a survey.