Public and private organizations are increasingly implementing various algorithmic decision-making systems. Through legal and practical incentives, humans will often need to be kept in the loop of such decision-making to maintain human agency and accountability, provide legal safeguards, or perform quality control. Introducing such human oversight results in various forms of semi-automated, or hybrid decision-making – where algorithmic and human agents interact. Building on previous research we illustrate the legal dependencies forming an impetus for hybrid decision-making in the policing, social welfare, and online moderation contexts. We highlight the further need to situate hybrid decision-making in a wider legal environment of data protection, constitutional and administrative legal principles, as well as the need for contextual analysis of such principles. Finally, we outline a research agenda to capture contextual legal dependencies of hybrid decision-making, pointing to the need to go beyond legal doctrinal studies by adopting socio-technical perspectives and empirical studies.