Measurement of gene expression levels and detection of eQTLs (expression quantitative trait loci) are difficult in tissues with limited sample availability, such as the brain. However, eQTL overlap between tissues might be high, which would allow for inference of eQTL functioning in the brain via eQTLs detected in readily accessible tissues, e.g. whole blood. Applying Stratified Linkage Disequilibrium Score Regression (SLDSR), we quantified the enrichment in polygenic signal of blood and brain eQTLs in genome-wide association studies (GWAS) of 11 complex traits. We looked at eQTLs discovered in 44 tissues by the Genotype-Tissue Expression (GTEx) consortium and two other large representative studies, and found no tissue-specific eQTL effects. Next, we integrated the GTEx eQTLs with regions associated with tissue-specific histone modifiers, and interrogated their effect on rheumatoid arthritis and schizophrenia. We observed substantially enriched effects of eQTLs located inside regions bearing modification H3K4me1 on schizophrenia, but not rheumatoid arthritis, and not tissue-specific. Finally, we extracted eQTLs associated with tissue-specific differentially expressed genes and determined their effects on rheumatoid arthritis and schizophrenia, these analysis revealed limited enrichment of eQTLs associated with gene specifically expressed in specific tissues. Our results pointed to strong enrichment of eQTLs in their effect on complex traits, without evidence for tissue-specific effects. Lack of tissue-specificity can be either due to a lack of statistical power or due to the true absence of tissue-specific effects. We conclude that eQTLs are strongly enriched in GWAS signal and that the enrichment is not specific to the eQTL discovery tissue. Until sample sizes for eQTL discovery grow sufficiently large, working with relatively accessible tissues as proxy for eQTL discovery is sensible and restricting lookups for GWAS hits to a specific tissue for which limited samples are available might not be advisable.