Circulating tumor cells (CTCs) are malignant cells released into the bloodstream with the potential to form metastases in secondary sites. These cells, acquired non-invasively, represent a sample of highly relevant tumor tissue that is an alternative to difficult and low-yield tumor biopsies. In recent years, there has been growing interest in genomic profiling of CTCs to enable longitudinal monitoring of the tumor's adaptive response to therapy. However, due to their extreme rarity, genotyping CTCs has proved challenging. Relevant mutations can be masked by leukocyte contamination in isolates. Heterogeneity between subpopulations of tumor cells poses an additional obstacle. Recent advances in single-cell sequencing can overcome these limitations but isolation of single CTCs is prone to cell loss and is prohibitively difficult and time consuming. To address these limitations, we developed a single cell sample preparation and genome sequencing pipeline that combines biophysical enrichment and single cell isolation using laser capture microdissection (LCM). A key component of this process is the encapsulation of enriched CTC sample in a hydrogel matrix, which enhances the efficiency of single-cell isolation by LCM, and is compatible with downstream sequencing. We validated this process by sequencing of single CTCs and cell free DNA (cfDNA) from a single patient with castration resistant prostate cancer. Identical mutations were observed in prostate cancer driver genes (TP53, PTEN, FOXA1) in both single CTCs and cfDNA. However, two independently isolated CTCs also had identical missense mutations in the genes for ATR serine/threonine kinase, KMT2C histone methyltransferase, and FANCC DNA damage repair gene. These mutations may be missed by bulk sequencing libraries, whereas single cell sequencing could potentially enable the characterization of key CTC subpopulations that arise during metastasis.