Background: Covid-status certification – certificates for those who test negative for the SARS-CoV-2 virus, test positive for antibodies, or who have been vaccinated against SARS-CoV-2 – has been proposed to enable safer access to a range of activities. Realising these benefits will depend in part upon the behavioural and social impacts of certification. The aim of this rapid review was to describe public attitudes towards certification, and its possible impact on uptake of testing and vaccination, protective behaviours, and crime. Method: A search was undertaken in peer-reviewed databases, pre-print databases, and the grey literature, from 2000 to December 2020. Studies were included if they measured attitudes towards or behavioural consequences of health certificates based on one of three indices of Covid-19 status: test-negative result for current infectiousness, test-positive for antibodies conferring natural immunity, or vaccination(s) conferring immunity. Results: Thirty-three papers met the inclusion criteria, only three of which were rated as low risk of bias. Public attitudes were generally favourable towards the use of immunity certificates for international travel, but unfavourable towards their use for access to work and other activities. A significant minority was strongly opposed to the use of certificates of immunity for any purpose. The limited evidence suggested that intention to get vaccinated varied with the activity enabled by certification or vaccination (e.g., international travel). Where vaccination is seen as compulsory this could lead to unwillingness to accept a subsequent vaccination. There was some evidence that restricting access to settings and activities to those with antibody test certificates may lead to deliberate exposure to infection in a minority. Behaviours that reduce transmission may decrease upon health certificates based on any of the three indices of Covid-19 status, including physical distancing and handwashing. Conclusions: The limited evidence suggests that health certification in relation to COVID-19 – outside of the context of international travel – has the potential for harm as well as benefit. Realising the benefits while minimising the harms will require real-time evaluations allowing modifications to maximise the potential contribution of certification to enable safer access to a range of activities.