Build Health Care Equipment in America Act This bill provides for certain tax incentives to combat COVID-19 (i.e., coronavirus disease 2019). Specifically, it (1) allows a bonus depreciation allowance for property used solely for the production or manufacturing of medical equipment to combat COVID-19, (2) a new payroll tax credit related to the employment of certain skilled health care workers who previously worked in a declining field, (3) requires the Department of the Treasury to publish a list of any occupation or field of work that qualifies as a medical short supply field, (4) increases education-related tax benefits for medical professionals in short supply, and (5) establishes the 21st Century Technology Fund for State and Local Governments Looking to Draw Businesses to Their Rural Regions.