Although person or identity verification has been predominantly explored using individual modalities such as face and voice, audio-visual fusion has recently shown immense potential to outperform unimodal approaches. Audio and visual modalities are often expected to pose strong complementary relationships, which plays a crucial role in effective audio-visual fusion. However, they may not always strongly complement each other, they may also exhibit weak complementary relationships, resulting in poor audio-visual feature representations. In this paper, we propose a Dynamic Cross-Attention (DCA) model that can dynamically select the cross-attended or unattended features on the fly based on the strong or weak complementary relationships, respectively, across audio and visual modalities. In particular, a conditional gating layer is designed to evaluate the contribution of the cross-attention mechanism and choose cross-attended features only when they exhibit strong complementary relationships, otherwise unattended features. Extensive experiments are conducted on the Voxceleb1 dataset to demonstrate the robustness of the proposed model. Results indicate that the proposed model consistently improves the performance on multiple variants of cross-attention while outperforming the state-of-the-art methods.