Sleep apnoea is a sleep breathing disorder which causes changes in cardiac and neuronal activity and discontinuities in sleep pattern when observed via electrocardiogram (ECG) and electroencephalogram (EEG). Using both statistical analysis and Gaussian discriminative modelling approaches, this paper presents a pilot study of assessing the cross-correlation between EEG frequency bands and heart rate variability (HRV) in normal and sleep apnoea clinical patients. For the study we used EEG (delta, theta, alpha, sigma and beta) and HRV (LF(nu), HF(nu) and LF/HF) features from the spectral analysis. The statistical analysis in different sleep stages highlighted that in sleep apnoea patients, the EEG delta, sigma and beta bands exhibited a strong correlation with HRV features. Then the correlation between EEG frequency bands and HRV features were examined for sleep apnoea classification using univariate and multivariate Gaussian models (UGs and MGs). The MG outperformed the UG in the classification. When EEG and HRV features were combined and modelled with MG, we achieved 64% correct classification accuracy, which is 2 or 8% improvement with respect to using only EEG or ECG features. When delta and acceleration coefficients of the EEG features were incorporated, then the overall accuracy improved to 71%.