Single-cell genomics and single-cell transcriptomics have emerged as powerful tools to study the biology of single cells at a genome-wide scale. However, a major challenge is to sequence both genomic DNA and mRNA from the same cell, which would allow direct comparison of genomic variation and transcriptome heterogeneity. We describe a quasilinear amplification strategy to quantify genomic DNA and mRNA from the same cell without physically separating the nucleic acids before amplification. We show that the efficiency of our integrated approach is similar to existing methods for single-cell sequencing of either genomic DNA or mRNA. Further, we find that genes with high cell-to-cell variability in transcript numbers generally have lower genomic copy numbers, and vice versa, suggesting that copy number variations may drive variability in gene expression among individual cells. Applications of our integrated sequencing approach could range from gaining insights into cancer evolution and heterogeneity to understanding the transcriptional consequences of copy number variations in healthy and diseased tissues.