Multi-modal test-time adaptation (MM-TTA) is proposed to adapt models to an unlabeled target domain by leveraging the complementary multi-modal inputs in an online manner. Previous MM-TTA methods rely on predictions of cross-modal information in each input frame, while they ignore the fact that predictions of geometric neighborhoods within consecutive frames are highly correlated, leading to unstable predictions across time. To fulfill this gap, we propose ReLiable Spatial-temporal Voxels (Latte), an MM-TTA method that leverages reliable cross-modal spatial-temporal correspondences for multi-modal 3D segmentation. Motivated by the fact that reliable predictions should be consistent with their spatial-temporal correspondences, Latte aggregates consecutive frames in a slide window manner and constructs ST voxel to capture temporally local prediction consistency for each modality. After filtering out ST voxels with high ST entropy, Latte conducts cross-modal learning for each point and pixel by attending to those with reliable and consistent predictions among both spatial and temporal neighborhoods. Experimental results show that Latte achieves state-of-the-art performance on three different MM-TTA benchmarks compared to previous MM-TTA or TTA methods.