Multi-modal object Re-IDentification (ReID) is devoted to retrieving specific objects through the exploitation of complementary multi-modal image information. Existing methods for multi-modal object ReID mainly concentrate on the fusion of multi-modal features, yet neglecting the background interference. Besides, current multi-modal fusion methods often focus on aligning modality pairs but suffer from multi-modal consistency alignment. To address these issues, we propose a novel selective interaction and global-local alignment framework called \textbf{Signal} for multi-modal object ReID. Specifically, we first propose a Selective Interaction Module (SIM) to select important patch tokens with intra-modal and inter-modal information. These important patch tokens engage in the interaction with class tokens, thereby yielding more discriminative features. Then, we propose a Global Alignment Module (GAM) to simultaneously align multi-modal features by minimizing the volume of 3D polyhedra in the Gramian space. Meanwhile, we propose a Local Alignment Module (LAM) to align local features in a shift-aware manner. With these modules, our proposed framework could extract more discriminative features for object ReID. Extensive experiments on three multi-modal object ReID benchmarks (i.e., RGBNT201, RGBNT100, MSVR310) validate the effectiveness of our method. The source code is available at .