Health Standards To Advance Transparency, Integrity, Science, Technology Infrastructure, and Confidential Statistics Act of 2021 or the Health STATISTICS Act of 2021 This bill requires efforts to standardize reporting of public health data, including for COVID-19 (i.e., coronavirus disease 2019) data. It also expands access to federal databases for health research. Specifically, the Centers for Disease Control and Prevention (CDC) must develop uniform standards for health departments and other entities that report public health data. The Department of Health and Human Services (HHS) may award grants to entities for adopting the uniform standards and otherwise improving their reporting capabilities. Furthermore, the CDC must, in consultation with the National Institutes of Health, establish specific standards within 30 days for reporting COVID-19 data. HHS must also disseminate this data subject to privacy and other requirements. Additionally, the Office of Management and Budget must issue guidance on federal health data collection that covers, for example, ensuring data quality and increasing access to health data for research. The National Center for Health Statistics (NCHS) must carry out a demonstration program to expand an existing program that links different federal data sets for statistical public health research, including research on food insecurity, housing instability, and other social determinants of health. In particular, the program must link to the National Death Index, a database of death records maintained by the NCHS. Finally, the bill requires the CDC to award grants to research entities and public health departments to increase their capacity for conducting statistical public health research.