This is one of the more obvious proofs of the cover-up. The FBI knew full well that Connally's shirt and coat were crucial forensic evidence, yet for months--not weeks, but months--both the FBI and the Secret Service acted as though Connally's clothes did not exist and showed no interest in them.
Nellie Connally notified the FBI and the Secret Service that she had her husband's bloody clothes, but, she said, "nobody seemed interested." She waited two months after notifying the FBI and the Secret Service, and then she decided to have them cleaned because she logically thought that for some reason there was no interest in them.
Finally, the FBI went and got the clothes from Mrs. Connally, and the FBI lab received them on April 1, 1964, but, as mentioned, Mrs. Connally had already had them cleaned, so they were of very limited forensic value. The holes could not be tested for metallic residue, not even by super-sensitive methods, and the value of the fabric and shape of the clothing holes was diminished.
Why the keystone-cop lack of interest? One reason was that the FBI was aware that both of Connally's surgeons suspected that the bullet that hit Connally had fragmented, which would explain the weird H-shaped tears in the front of the shirt and the dimensions and nature of the wrist wounds.
Another reason for the astonishing months-long lack of interest was that the FBI knew that spectrographic testing of the Connally clothing holes could reveal metallic residues that were different in composition from the residues found on the edges of the holes in the back of JFK's shirt and coat, which of course would prove that Connally and JFK were hit by different bullets.