Yes, there is almost certainly a genetic overlap between schizophrenia and OCD.
Quantifying the overlap in variation requires genotyping a large number of individuals, and a lot of this cross-disorder work is done by consortia. The Cross-Disorder Group of the Psychiatric Genomics Consortium estimated the genetic correlation due to common polymorphisms between ADHD (attention deficit hyperactivity), BPD (bipolar), SCZ (schizophrenia), MDD (major depression), and ASD (autism spectrum) (Wray, N.R. et al. 2013). Their key findings may interest you:
The genetic correlation calculated using common SNPs was high between schizophrenia and bipolar disorder (0.68 ± 0.04 s.e.), moderate between schizophrenia and major depressive disorder (0.43 ± 0.06 s.e.), bipolar disorder and major depressive disorder (0.47 ± 0.06 s.e.), and ADHD and major depressive disorder (0.32 ± 0.07 s.e.), low between schizophrenia and ASD (0.16 ± 0.06 s.e.) and non-significant for other pairs of disorders as well as between psychiatric disorders and the negative control of Crohn's disease.
But OCD wasn't on their list, likely because not as many cases have been genotyped for OCD as for the five disorders listed. A review in Science from 2015 shows the number of cases involved in the largest genome-wide association study for each of 13 classes of psychiatric disorder at that time, including OCD, for which 1,889 subjects had been genotyped (Geschwind, D. H. & Flint, J., 2015). Most likely, as the sample size of OCD cases increases, OCD will be incorporated into the PGC's cross-disorder studies.
A recent study used the PGC SCZ data plus data collected from 370 Spanish OCD cases to estimate the shared polygenic risk between the two disorders. They claim that SCZ polygenic risk from the PGC data explains 3.7% of the phenotypic variance in their OCD data, which represents an overlap in the genetics (Costas, J., et al., 2016).
This study's results likely underestimate the true genetic correlation between the disorders for two reasons: 1) the sample sizes to date for OCD have been too small to identify genome-wide significant GWAS hits, so our understanding of OCD genetics still has quite a way to go, and 2) this study focused on exonic regions, while most of the polygenic risk for psychiatric disease is not found in exons.
Costas, J., Carrera, N., Alonso, P., Gurriarán, X., Segalàs, C., Real, E., López-Solà, C., Mas, S., Gassó, P., Domènech, L., Morell, M., Quintela, I., Lázaro, L., Menchón, J. M., Estivill, X. & Carracedo, Á., 2016. Exon-focused genome-wide association study of obsessive-compulsive disorder and shared polygenic risk with schizophrenia. Translational Psychiatry, 6(768).
Geschwind, Daniel H. & Flint J., 2015. Genetics and genomics of psychiatric disease. Science 349(6255), pp. 1489-1494.
Wray, Naomi R. and The Cross-Disorder Group of the Psychiatric Genomics Consortium, 2013. Genetic relationship between five psychiatric disorders estimated from genome-wide SNPs. Nature Genetics 45, pp. 984–994