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Genetic variants disrupting DNA methylation at CpG dinucleotides (CpG-SNP) provide a set of known causal variants to serve as models for testing fine-mapping methodology. We use 1716 CpG-SNPs to test three fine-mapping approaches (BIMBAM, BSLMM, and the J-test), assessing the impact of imputation errors and the choice of reference panel by using both whole-genome sequence (WGS), and genotype array data on the same individuals (n=1166). The choice of imputation reference panel had a strong effect on imputation accuracy, with the 1000 Genomes Phase 3 (1000G) reference panel (n=2504 from 26 populations) giving a mean non-reference discordance rate between imputed and sequenced genotypes of 3.2% compared to 1.6% when using the Haplotype Reference Consortium (HRC) reference panel (n=32470 Europeans). These imputation errors impacted on whether the CpG-SNP was included in the 95% credible set, with a difference of ∼ 23% and ∼ 7% between the WGS and the 1000G and HRC imputed datasets respectively. All of the fine-mapping methods failed to reach the expected 95% coverage of the CpG-SNP. This is attributed to secondary cis genetic effects that are unable to be statistically separated from the CpG-SNP, and through a masking mechanism where the effect of the methylation disrupting allele at the CpG-SNP is hidden by the effect of a nearby SNP that has strong LD with the CpG-SNP. The reduced accuracy in fine-mapping a known causal variant in a low level biological trait with imputed genetic data has implications for the study of higher order complex traits and disease.