COVID-19 Emergency Production Act This bill directs the President to use existing authorities under the Defense Production Act of 1950 with respect to the production of COVID-19 (i.e., coronavirus disease 2019) supplies, such as personal protective equipment, diagnostic tests, and vaccines. That act confers upon the President a broad set of authorities to influence domestic industry in order to provide essential materials and goods needed for the national defense. Specifically, the President must (1) make a determination that such supplies are essential for the national defense, (2) identify private-sector capacity to produce these supplies, and (3) exercise authorities under the act to require emergency production of them at a reasonable price. In addition, the President shall coordinate the allocation of these supplies based on requests from governors and the needs of the states as determined by the population of each state. The bill's directive to produce COVID-19 supplies terminates when there are no remaining requests for them from states, and supplies that have been produced but are unused at that time shall be deposited into the Strategic National Stockpile.