It would be beneficial to find genetic predictors of antidepressant response to help personalise treatment of major depressive disorder (MDD). Rare copy number variants (CNVs) have been implicated in several psychiatric disorders, including MDD, but their role in antidepressant response has yet to be investigated. CNV data were available for 1565 individuals with MDD from the NEWMEDS (Novel Methods leading to New Medications in Depression and Schizophrenia) consortium with prospective data on treatment outcome with either a serotonergic or noradrenergic antidepressant. No association was seen between the presence of CNV (rare or common), the overall number of CNVs or genomic CNV 'burden' and antidepressant response. Specific CNVs were nominally associated with antidepressant response, including 15q13.3 duplications and exonic NRXN1 deletions. These were associated with poor response to antidepressants. Overall burden of CNVs is unlikely to contribute to personalising antidepressant treatment. Specific CNVs associated with antidepressant treatment require replication and further study to confirm their role in the therapeutic action of antidepressant.