Emerging spatial technologies including spatial transcriptomics and spatial epigenomics are becoming powerful tools for profiling cellular states in the tissue context. However, current methods capture only one layer of omics information at a time precluding the possibility to examine the mechanistic relationship across the cental dogma of molecular biology. Here, we present two spatial multi-omics technologies for spatially resolved genome-wide joint mapping of epigenome and transcriptome by coprofiling chromatin accessibility and gene expression (spatial-ATAC-RNA-seq) or histone modification and gene expression (spatial-CUT\&Tag-RNA-seq) on the same tissue section at a resolution near single cells. They were applied to embryonic and neonatal mouse brain as well as adult human brain to map how epigenetic states or modifications regulate cell type and dynamics in tissue. Although distinct tissue features were identified by either spatial epigenome or spatial transcriptome alone with high concordance, we observed their differential roles in defining cell states. In general, epigenetic state proceeds the development of transcriptional phenotype in relation to epigenetic lineage priming. We also observed high expression canonical markers such as PROX1 in the granular cell layer of the human hippocampus showed low chromatin accessibility that corresponded to a low level of RNA turnover rate, highlighting a divergent need for open chromatin or transcription to control cell identity and dynamics. Spatial epigenome-transcriptome co-profiling is a highly informative tool to study the mechanism of gene expression regulation in tissue and may enable a wide range of applications in life science and biomedical research.