Did he delete a file that was located on the server? Or delete a file that was located on his client?
If it was located on the server, the log.nsf should record that information. For example, I deleted a file yesterday:
10/14/2014 12:39:37 Database mail\xxxxxxxxx.nsf deleted by Mark A Taylor/xxxxxxxxxx/North America/xxxxxxxxx
In order for a user to delete the file, they'd have to have Manager access to that file.
If the file was located on the client, I would expect that the client's log.nsf or Console.log (if enabled) would show it.