Population-scale resources of genetic, molecular, and cellular information form the basis for understanding human genomes, charting the heritable basis of disease and tracing the effects of mutations. Pooled perturbation assays, probing the effect of many perturbations coupled with single-cell RNA sequencing (scRNA-seq) readout, are especially potent references for interpreting disease-linked mutations or gene-expression changes. However, the utility of existing maps has been limited by the comprehensiveness of perturbations conducted and the relevance of their cell-line context. Here, we present a genome-scale CRISPR interference perturbation map with scRNA-seq readout across many genetic backgrounds in human pluripotent cells. We map trans expression changes induced by knockdowns and characterize their variation across donors, with expression quantitative trait loci linked to higher genetic modulation of perturbation effects. This study pioneers population-scale CRISPR perturbations with high-dimensional readouts, which will fuel the future of effective modulation of cellular disease phenotypes.