In the present work, a first-principles investigation of electric-field gradients ͑EFG's͒ at the Cd site for possible neutral complexes of Cd-H in crystalline silicon has been performed. This was motivated by experimental results observed by perturbed angular correlation spectroscopy, and with the aim of trying to establish the validity of the configurational models proposed in the literature. We use the full-potential linear-muffintin-orbital method, within the local-density functional theory, and the supercell approach. We have allowed local relaxations of the Cd and Si nearest and next-nearest neighbors for different positions of H in the high and low electron-density regions. We have found that H in an intrabond site is unstable ͑saddle point͒, and that a bridgelike configuration is the energetically favorable one, where the Cd atom and the nearest silicon suffer relaxations along the ͓111͔ direction. The antibond positions of low electronic density regions were also studied, and have been found to be also local minima. The calculated EFG's in these configurations that locally minimize the total energy of the supercell ͑H at bridgelike and H in antibond sites to Cd and Si 1 ͒ give quadrupolar coupling constants which are in agreement with the experimental results. ͓S0163-1829͑98͒06415-7͔