Social media are important channels for crisis and risk communication by government agencies. However, existing frameworks for studying these messages use loose and inconsistent terminology, making it difficult to build on this research and understand how message features impact message diffusion. In this study, we provide a framework based on textual and media dimensions of messages for improved analysis of social media crisis and risk communication. We apply the framework to a sample of Twitter posts from United States local, state and federal public health agencies during a year of the Covid-19 pandemic. Results show reasonable reliability levels for coding of message features; differences and similarities of messages across local, state and federal public health agencies; and significant associations between message features and message diffusion. The study contributes to research on crisis and risk messages, and our understanding of the impacts of message features on message diffusion.