We use ATAC-seq to examine chromatin accessibility for four different tissues inDrosophila melanogaster: adult female brain, ovaries, and both wing and eye-antennal imaginal discs from males. Each tissue is assayed in eight different inbred strain genetic backgrounds, seven associated with a reference quality genome assembly. We develop a method for the quantile normalization of ATAC-seq fragments and test for differences in coverage among genotypes, tissues, and their interaction at 44099 peaks throughout the euchromatic genome. For the strains with reference quality genome assemblies, we correct ATAC-seq profiles for read mis-mapping due to nearby polymorphic structural variants (SVs). Comparing coverage among genotypes without accounting for SVs results in a highly elevated rate (55%) of identifying false positive differences in chromatin state between genotypes. After SV correction, we identify 1050, 30383, and 4508 regions whose peak heights are polymorphic among genotypes, among tissues, or exhibit genotype-by-tissue interactions, respectively. Finally, we identify 3988 candidate causative variants that explain at least 80% of the variance in chromatin state at nearby ATAC-seq peaks.