There might be a PCB/board id printed on the board, but I don't recall if those are device-specific, they might instead be revision-specific instead (although, a random look at the one on my K4 makes it look fairly specific). The S/N used to be printed on the *box*, though, but that doesn't help you ;p.
Not that that would help much, either, as you probably have no idea what your board id actually was
.
The RFID chip stuck on the inside of the back cover *might* have more detailed data, though, but I have no idea how you might read those things
.
I explicitly said root/shell access and not JB, because while, yeah, a JailBroken device would make it easier, it's not necessarily the only way.
Sidebar: That's some very dedicated police officers you've got there, I wouldn't have expected that ;p.