The males and females of the brine shrimp Artemia franciscana are highly dimorphic, and this dimorphism is associated with substantial sex-biased gene expression in heads and gonads. How these sex-specific patterns of expression are regulated at the molecular level is unknown. A. franciscana also has differentiated ZW sex chromosomes, with complete dosage compensation, but the molecular mechanism through which compensation is achieved is unknown. Here, we conducted CUT&TAG assays targeting 7 post-translational histone modifications (H3K27me3, H3K9me2, H3K9me3, H3K36me3, H3K27ac, H3K4me3, and H4K16ac) in heads and gonads of A. franciscana, allowing us to divide the genome into 12 chromatin states. We further defined functional chromatin signatures for all genes, which were correlated with transcript level abundances. Differences in the occupancy of the profiled epigenetic marks between sexes were associated with differential gene expression between males and females. Finally, we found a significant enrichment of the permissive H4K16ac histone mark in the Z-specific region in both tissues of females but not males, supporting the role of this histone mark in mediating dosage compensation of the Z chromosome.