You can take a look at your users's .bash_history, assuming they use bash:
Code:
cd /home
find `ls`/.bash_history -exec /usr/bin/grep "deleted-filename" {} /dev/null \;
If it's a file that only root can delete then look at root's .bash_history, but then you have to find out who was logged as root or su'ed to root. For this the command "last root|more" could help you