The properties of turbulent electroconvective fluctuations generated in a nematic liquid crystal under the action of an external oscillating electric field are investigated. In particular, the spectral properties and the scaling behaviour of probability density functions (PDFs) of light intensity fluctuations are considered at different voltages. At intermediate voltage, in the weak turbulent regime, PDFs are Gaussian at large scales and show increasingly enhanced wings at smaller scales, recalling the typical signature of intermittency in isotropic fluid flows. When the voltage is increased, dynamical scattering regimes appear, characterized by increasing complexity. In order to get a quantitative estimate of intermittency, PDFs are modeled through the Castaing distribution, and structure functions are estimated in the framework of Extended Self-Similarity. Results support the generation of small-scale fluctuations through a fragmentation process of large-scale structures. The persistent anisotropic properties of the fluctuations are highlighted by the results.