Neural machine translation (NMT) systems have been gradually integrated into institutional translation workflows, together with other tools. As most NMT systems are trained based on publicly-available textual data, the question arises as to whether there are any significant differences between NMT and human translations of institutional texts, or particular patterns that NMT developers should take into account. In the case of legal translation, previous research has pointed to legal terminology as a major weakness of NMT. From the perspective of artificial intelligence, law and translation studies, it is particularly relevant to explore quality variations that may be associated to issues of legal asymmetry when translating legal terms. This is the central theme of the paper: is legal singularity a major obstacle for NMT, as it is a frequent difficulty for human translators? Are translation accuracy and consistency impacted by the higher translation difficulty generally associated with more singular legal terms? To answer these questions, the study compares the performance of human translators and three NMT systems (Google Translate, DeepL and Systran Translate) in terms of translation accuracy and intratextual consistency in text samples from the main European Union institutions, the United Nations and the World Trade Organization. It presents a mixed analysis of the French and Spanish translations of five English source terms that are considered representative of various levels of legal singularity: “court of appeal”, “high court”, “magistrates court”, “due process” and “prima facie evidence”. Given the importance of legal terminology for ensuring legal certainty and reliability in multilingual law, this research highlights the implications of using NMT to translate institutional legal texts, and the quality issues to be addressed in these settings by both NMT system developers and translators in a context of increasing human-machine interaction.