In the sniper's nest, there were four boxes used in connection with the shooting. One large box containing books and then two of the smaller "Rolling Readers" boxes atop the large box of books. The fourth box was on the floor behind the stack of three,
obviously used as a seat.
On one of the Rolling Readers boxes at the window, Oswald's left palmprint and his right index fingerprint were found.
The employees laying the floor moved the large boxes of books from the west end of the floor over to the east end. However, the "Rolling Readers" boxes did not need to be moved, i.e. they weren't over on the west end where the new floor was being placed down. The two "Rolling readers" boxes in the sniper's nest were originally about three aisles over from the sniper's nest window and were taken to that window for the purposes of being used as a gun rest. The "Rolling Readers" boxes didn't contain books.
On the box on the floor, the one used as a seat, Day, using powder, dusted the box and developed a palmprint. Latona examined the print and found it to be from Oswald's right palm. Because Day used a powder to develop the print, Latona stated that not too long a time had passed between the time the print was placed on the box and the time it was developed by Day. Powder cannot develop prints beyond a certain point in time.
FBI experiments showed that twenty-four hours was a likely maximum time between the print being placed on the box and the time it was developed by the powder. However, Latona would only state that he could only testify with certainty that the print was less than three days old.
Arthur Mandella (fingerprint expert, NYPD), examined the prints and agreed that they belonged to Oswald. Mandella was of the opinion that the palmprint developed by Day (using the powder) from the box on the floor (the one used as a seat) was probably made within a day to a day and a half of the examination made on the 22nd.
Oswald could obviously have handled the boxes as part of his normal work duties. Fingerprints were taken from the twelve Depository employees who may have had cause to handle the boxes (found in the sniper's nest) as part of their normal work duties as well.
Other identifiable prints were developed on the boxes. These prints were compared with the fingerprints of all other employees as well as law enforcement personnel who handled the boxes. None of the identifiable prints belonged to any of the other employees.
Point being, the larger box on the sniper's nest floor used as a seat, was moved by the floor laying crew at some point earlier in the week. Day dusted this box with powder and developed a palmprint, which Latona said belonged to Oswald. The process of using the powder develops prints based on perspiration and therefore would not find prints older than one to three days (time frame dependent on which fingerprint expert you listen to).
While it's possible to handle the boxes and not leave a print at all, it's also likely as possible that Oswald was the only person to handle that box at any point in time past Tuesday the 19th (per Latona's three days out). Or, if you go by Mandella of the NYPD, Oswald could have been the only person to handle that box after Wednesday the 20th. If you go by the FBI's experiments, Oswald was possibly the only person to handle that box after Thursday the 21st.
Oswald's prints on the boxes prove he was in that window, but they can't prove when he was there exactly.