Effective interpretation of genome function and genetic variation requires a shift from epigenetic mapping of cis-regulatory elements (CREs) to characterization of endogenous function. We developed HCR-FlowFISH, a broadly applicable approach to characterize CRISPR-perturbed CREs via accurate quantification of native transcripts, alongside CASA (CRISPR Activity Screen Analysis), a hierarchical Bayesian model to quantify CRE activity. Across >325,000 perturbations, we provide evidence that CREs can regulate multiple genes, skip over the nearest gene, and can display activating and/or silencing effects. At the cholesterol-level associated FADS locus, we combine endogenous screens with reporter assays to exhaustively characterize multiple genome-wide association signals, functionally nominating causal variants and importantly, identifying their target genes.