April 2, 2012, at 9 a.m., is correct. But you must know your ancestors' Enumeration District (where they were living) that year, because the census won't be searchable (indexed by name, etc.) like the other available years are now. That'll take awhile.

The links provided here show how to prepare for the 1940 Census release and how you can help index.

http://1940census.archives.gov/

http://www.archives.gov/research/census/1940/start-research.html