Multimodal analysis has recently drawn much interest in affective computing, since it can improve the overall accuracy of emotion recognition over isolated uni-modal approaches. The most effective techniques for multimodal emotion recognition efficiently leverage diverse and complimentary sources of information, such as facial, vocal, and physiological modalities, to provide comprehensive feature representations. In this paper, we focus on dimensional emotion recognition based on the fusion of facial and vocal modalities extracted from videos, where complex spatiotemporal relationships may be captured. Most of the existing fusion techniques rely on recurrent networks or conventional attention mechanisms that do not effectively leverage the complimentary nature of audio-visual (A-V) modalities. We introduce a cross-attentional fusion approach to extract the salient features across A-V modalities, allowing for accurate prediction of continuous values of valence and arousal. Our new cross-attentional A-V fusion model efficiently leverages the inter-modal relationships. In particular, it computes cross-attention weights to focus on the more contributive features across individual modalities, and thereby combine contributive feature representations, which are then fed to fully connected layers for the prediction of valence and arousal. The effectiveness of the proposed approach is validated experimentally on videos from the RECOLA and Fatigue (private) data-sets. Results indicate that our cross-attentional A-V fusion model is a cost-effective approach that outperforms state-of-the-art fusion approaches. Code is available: \url{https://github.com/praveena2j/Cross-Attentional-AV-Fusion}