Tampon Safety and Research Act of 1999 - Amends the Public Health Service Act to mandate the conduct or support of research on the extent to which additives in feminine hygiene products pose any risks to the health of women or to the children of women who use those products during or before the pregnancies involved. Requires that the research include research to confirm the data on feminine hygiene products submitted to the Commissioner of Food and Drugs by manufacturers of the products. Requires that research results be submitted to the Congress, specified governmental agencies, and the public.