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Disease risk alleles influence the composition of cells present in the body, but modeling genetic effects on the cell states revealed by single-cell profiling is difficult because variant-associated states may reflect diverse combinations of the profiled cell features that are challenging to predefine. We introduce Genotype-Neighborhood Associations (GeNA), a statistical tool to identify cell-state abundance quantitative trait loci (csaQTLs) in high-dimensional single-cell datasets. Instead of testing associations to predefined cell states, GeNA flexibly identifies the cell states whose abundance is most associated with genetic variants. In a genome-wide survey of single-cell RNA sequencing peripheral blood profiling from 969 individuals, GeNA identifies five independent loci associated with shifts in the relative abundance of immune cell states. For example, rs3003-T (P = 1.96 × 10) associates with increased abundance of natural killer cells expressing tumor necrosis factor response programs. This csaQTL colocalizes with increased risk for psoriasis, an autoimmune disease that responds to anti-tumor necrosis factor treatments. Flexibly characterizing csaQTLs for granular cell states may help illuminate how genetic background alters cellular composition to confer disease risk.