Riemannian neural networks, which generalize the deep learning paradigm to non-Euclidean geometries, have garnered widespread attention across diverse applications in artificial intelligence. Among these, the representative attention models have been studied on various non-Euclidean spaces to geometrically capture the spatiotemporal dependencies inherent in time series data, e.g., electroencephalography (EEG). Recent studies have highlighted the full-rank correlation matrix as an advantageous alternative to the covariance matrix for data representation, owing to its invariance to the scale of variables. Motivated by these advancements, we propose the Correlation Attention Network (CorAtt) tailored for full-rank correlation matrices and implement it under the permutation-invariant and computationally efficient Off-Log and Log-Scaled geometries, respectively. Extensive evaluations on three benchmarking EEG datasets provide substantial evidence for the effectiveness of our introduced CorAtt. The code and supplementary material can be found at https://github.com/ChenHu-ML/CorAtt.