Connected health applications encompass m-health, e-health and digital health applications. More and more healthcare professionals and patients are adopting connected health solutions. It is expected that the advances in the Information and Communication Technologies in healthcare services will keep increasing in the future. Given the deterioration of the environment a growing need to consider sustainability in technology is observed. Moreover, there is an increasing interest in software sustainability among the software engineering community. Software sustainability is about producing environment-friendly products to support sustainability goals. It aims also to achieve sustainable products that have limited impact on the environment. In this vein, an assessment method using a checklist for the software sustainability of connected health application is proposed in this paper. To this end, the individual, social, environmental and technical dimensions of software sustainability were considered. The checklist was generated from a reusable requirement catalog intended for sustainable connected health applications. In addition, the checklist artifact can serve as a tool to audit this kind of e-health applications in sustainability.