Pandemic School Nurse Training to Protect Students and Communities Act of 2020 This bill authorizes the Department of Health and Human Services to make grants to, and enter into contracts with, state and local education agencies to train elementary and secondary school nurses to serve as first responders and crisis managers in the event of a biological or chemical attack at a school or an outbreak of pandemic influenza among individuals under their care. The training must prepare school nurses to (1) protect and preserve life; (2) notify public health authorities to help contain or mitigate the effects of an attack or outbreak; and (3) take other appropriate and feasible actions, such as preserve evidence of an attack.