Because the Census Bureau does not collect vital statistics, you are unlikely to find birth and death data broken down by Census Tract.
Vital statistics are collected at the state level. To find information on Live Births and General Deaths in your community:
Like other vital statistics, information on Leading Causes of Death is collected by state health departments. Census Tract-level data is most likely unavailable.
To find information on deaths and death rates by selected causes by State and by County, see the tables that are available on the "Vital Statistics of New York State" page link above.
You may be able to find leading causes of death in your Community on local government Web sites. New York City, for example, publishes cause of death information for the city as a whole, and for various community districts, in the "Vital Statistics Summary."
For information on Non-Communicable Diseases, you will also want to check the State Health Department's Website, though you will need to look at the areas devoted to specific diseases for State and (sometimes) County data. Since there are no reporting requirements for non-communicable diseases, the data may or may not be available. See especially the following areas: