Understanding the role of genes and genetic variants is a key challenge in unraveling the driving mechanisms of Alzheimer's disease (AD). Single-cell RNA sequencing is a technique that quantifies gene expression at the cell (type) level enabling investigation of the roles of different cell types in disease. We analyzed changes in gene (co-)expression associated with genetic variants using single-cell RNA sequencing data (>1.3 million cells) from the dorsolateral prefrontal cortex (DLPFC) of 379 individuals of the ROSMAP cohort. Our single cell expression quantitative trait loci (sc-eQTL) analysis determined 3,337,065 sc-eQTLs, linking 1,882,645 SNPs to changes in expression of 8,057 genes in 7 major cell types. Next, we investigated the association of genetic variants with changes in co-expression for gene pairs (co-eQTLs), focusing on a set of variants and genes relevant to AD. Our novel non-parametric method for co-eQTL analysis compares gene co-expression distributions between SNP genotypes. We found 6,878 cell type specific co-eQTLs (variant-gene-gene combinations) relating to 18 AD variants. Although a substantial proportion of the findings is driven by eQTL effects, our method identified co-eQTLs that would not have been discovered in a correlation-based analysis. Most notable, we found variant rs13237518 (located in the TMEM106B gene) to associate with expression changes in a subset of 25 genes in excitatory neurons which is possibly indicative of higher-level disruptions related to the variant. Overall, we show that exploring genetic variant-associated changes in gene (co-)expression is a promising approach in finding cell type specific mechanisms that may be altered in AD.