The convictions of the two paramedics shook the world of emergency workers who have typically been shielded from criminal prosecution — and it forced questions about the dynamic between the police and paramedics at a scene.

Though Mr. McClain was visibly distressed and in handcuffs, paramedics never spoke to him, touched him or checked his vital signs before diagnosing him with excited delirium, a controversial condition characterized by agitation and exceptional physical strength. Paramedics then injected him with what authorities later said was a dose of ketamine inappropriate for Mr. McClain’s body weight.