Two sets of cross-correlated relaxation rates involving chemical shift anisotropy and dipolar interactions have been measured in an RNA kissing complex. In one case, both the CSA and dipolar interaction tensors are located on the same nucleotide base and are rigidly fixed with respect to each other. In the other case, the CSA tensor is located on the nucleotide base whereas the dipolar interaction is located on the adjoining ribose unit. Analysis of the measured rates in terms of isotropic or anisotropic rotational diffusion has been carried out for both cases. A marked difference between the two models is observed for the cross-correlation rates involving rigidly fixed spin interactions. The influence of internal motions about the glycosidic linkage between the nucleotide base and the ribose unit on cross-correlated relaxation rates has been estimated by applying a model of restricted rotational diffusion. Local motions seem to have a more pronounced effect on cross-correlated relaxation rates when the two spin interactions are not rigidly fixed with respect to each other.