Laboratory diagnosis of SARS-CoV-2 infection uses PCR to detect viral RNA (vRNA) in respiratory samples. While SARS-CoV-2 RNA has been detected in other sample types, there is very little understanding about its clinical or laboratory significance. This has implications for testing and for safe working in a laboratory setting. To answer this, we undertook a systematic review for evidence of viral RNA in blood. We also attempted viral isolation from PCR-positive blood samples. Viral RNA was detectable at very low levels, but this was not associated with infectious SARS-CoV-2. This work will help to inform biosafety precautions for handling blood from COVID-19 patients.