To avoid any misunderstandings I thought I would create this post for clarity on the subject.
The Bureau of Investigation (BOI - later renamed FBI) never had jurisdiction in this case - ever. After the crime there was an immediate offer of "assistance" which was accepted. The New Jersey State Police (NJSP) were, from the beginning to the end, in charge of this Case.
However, as criticism of the NJSP began to get louder, "in-fighting" among the various Agencies began. There were "unauthorized" interviews, evidence being witheld, jealousy, suspicion, alliances, and "misleading" information dealt with the specific intent to harm certain investigations conducted by specific Agencies and/or Individuals. In short, the NJSP did not want anyone but their Office "solving" the crime, Schwarzkopf's biggest fear was that his name would remain in the gutter while someone else grabbed all the glory.
As a resut, on several occasions, J. Edgar Hoover requested total withdrawal from the Case citing failure from other Agencies, namely the NJSP, to cooperate. The resulting move by the President was made on May 13, 1932 (the day after the child's corpse had been located) declairing that while the NJSP was in charge of this investigation and that all Government Agencies were at their disposal - the FBI were to be the "clearing house" for all the various Government Agencies. This meant that any or all information gained by an Investigative Government Agency (or otherwise) was first to be given to the FBI who would then turn it over to the NJSP.
Unfortunately, this order made by the President was generally ignored.
For example: "T-Man" Treaury Agent Frank Wilson (IRS) had been working hand in glove with the NJSP - specifically Lt. Keaton and actually became very good friends him as a result. He had failed to turn over any reports to the FBI prior to the Presidential Instruction on 5-13-32. Once the President instructed all Federal Agencies to turn over all information to the FBI, Wilson still failed to turn over any reports. Hoover then requested Wilson's written reports from Chief Elmer Irey on May 16, 1932 and it was explained that Wilson was "tied up" with the Curtis investigation and would "confer" at a later date to turn over the facts. I have found no evidence of this ever occurring. So sometime in September '33 Hoover had a personal meeting with the President to, once again, voice his concerns and request withdrawal. As a direct result of this meeting Homer S. Cummings, Attorney General was contacted and informed him that the President wanted the Treasury Department to turn over its information to the - now renamed - United States Bureau of Invetigation (USBOI) (renamed FBI). AG Cummings then wrote a letter to Guy Helvering, Commissioner of Internal Revenue, requesting the President's wishes be fulfilled. On 10-33 Special Agent Wilson was then ordered to make a final report and turn it over to the FBI. On 11-11-33, Wilson submitted this report which was turned over to J. Edgar Hoover. Agent Sisk, Division of Investigation (DOI) (renamed FBI) made the following in his report dated 6-8-34:
....Agent Wilson's report covering his investigation and also that of his Unit was received at the Division under date of November 11, 1933, and purported to cover the complete investigation during the period March 18, 1932 to October 14, 1933. A perusal of this report indicates that many material facts were omitted from same, and that many angles of the case worked by Wilson were not mentioned in his report.
Sisk continues on in this same report:
It has been previously shown that the Division was not at any time furnished with the basic facts relative to the Lindbergh kidnaping or with copies of the evidence in the case, although numerous requests, both oral and written, have been made upon the New Jersey State Police for this information. Under date of April 6, 1934 the Director addressed still another communication to Colonel Schwarzkopf requesting that the Division be furnished with all available evidence in connection with this case, so that the investigation could be conducted along intelligent lines, and so that the data might be compared with other data received in other kidnaping cases.
So one can plainly conclude the FBI never had any jurisdiction in this case other then some "leverage" gained by Presidential Order which was widely ignored and resisted. Once Hauptmann is arrested it only got worse.