Multimodal multi-label emotion recognition (MMER) aims to identify the concurrent presence of multiple emotions in multimodal data. Existing studies primarily focus on improving fusion strategies and modeling modality-to-label dependencies. However, they often overlook the impact of aleatoric uncertainty, which is the inherent noise in the multimodal data and hinders the effectiveness of modality fusion by introducing ambiguity into feature representations.To address this issue and effectively model aleatoric uncertainty, this paper proposes Latent emotional Distribution Decomposition with Uncertainty perception (LDDU) framework from a novel perspective of latent emotional space probabilistic modeling. Specifically, we introduce a contrastive disentangled distribution mechanism within the emotion space to model the multimodal data, allowing for the extraction of semantic features and uncertainty. Furthermore, we design an uncertainty-aware fusion multimodal method that accounts for the dispersed distribution of uncertainty and integrates distribution information. Experimental results show that LDDU achieves state-of-the-art performance on the CMU-MOSEI and M³ED datasets, highlighting the importance of uncertainty modeling in MMER. Code is available at https://github.com/201983290498/lddu_mmer.git.