Sorry, you are off by four years. Assuming a kidnapping actually occurred (there are theories that the baby died a few days earlier than reported by other means and that the kidnapping story was concocted by Lindbergh and friends and family as a cover-up), it was on March 1, 1932.
According to this book review which appeared on the Daily Caller the full details are now available and the case has been solved.
I read the Zorn book twice cover-to-cover and am not convinced at all he has solved the case. But I do appreciate the diligence of his work. (I have also read other materials on it in the past and saw the relatively new PBS Nova documentary on the case in which Zorn is a participant.). Zorn states that an erstwhile neighbor of his grandfather and his then teenage father in a German neighborhood in the Bronx, an immigrant by the name of John Knoll (who does not appear in any of the extensive official investigatory records), was the mastermind of the kidnapping and the man known as "Cemetery John," who received ransom money from an intermediary representing Lindbergh in a dark cemetery at night. But in order to implicate Knoll, he asks the reader to make too many leaps of faith, all too numerous to detail here. One of the most glaring is that the man receiving the ransom money ("Cemetery John") is immediately turned into a kidnapper, without considering the possibility that he could have been a clever extortionist, probably one of several in a group, who took advantage of the widely publicized event so as rip off Lindbergh without knowing anything about the fate of the baby.
This is a most fascinating mystery and it's unlikely to ever be solved to the satisfaction of most crime buffs. After all, it still provokes a wide range of opinion after 81 years.
If I said 1936 was date of kidnapping then I was in error. It was Hauptmann who died in 1936.