The NYC Department of Health makes data available to researchers and the public through various interactive tools. In addition the recently revamped the interactive EpiQuery tool, they launched the Community Health Profiles tool, which allows you to explore the health of your neighborhood and compare it with other communities across the city.
Information on Communicable Diseases must be reported to local health departments.
Statistics on communicable diseases at the State and County levels are available through the New York State Department of Health Website at http://www.health.state.ny.us/nysdoh/research/disease/disease.htm. See especially the "Communicable Disease in New York State Annual Reports".
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:
New York State Cancer Registry
Diabetes in New York State
Heart Disease Statistics
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 (http://www.health.state.ny.us/nysdoh/vital_statistics/index.htm).
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" (http://www.nyc.gov/html/doh/html/data/vs.shtml). If your local government does not provide cause of death data, try the Infoshare Database.