COVID-19 Workforce Emergency Response Act This bill increases flexibility for state and local agencies to provide continuity of services during the COVID-19 (i.e., coronavirus disease 2019) national emergency. In particular, the bill allows certain state and local unobligated funds to be used for administrative purposes to carry out local workforce investment activities under one-stop delivery systems if the funds are used to respond to such emergency. (A one-stop delivery system is a system under which entities responsible for administering separate workforce investment, educational, and other human resource programs and funding streams (referred to as one-stop partners) collaborate to create a seamless system of service delivery that will enhance access to the programs' services and improve long-term employment outcomes for individuals receiving assistance.) The bill also allows the use of certain state reserved unobligated funds for (1) responding to the national emergency, and (2) distributing by the governor of such state to local boards most impacted by the coronavirus for activities related to responding to such emergency. The Department of Labor must award national dislocated worker grants, with emphasis on state or local areas most impacted by the emergency for activities directly supporting the response to the emergency and related-recovery efforts (e.g., training and temporary employment and certain layoff response activities).