I think you should be upfront and honest about your background. They don't want officers who cover things up. They will ask on your background if you've ever taken anything from work and if you don't tell them and they find out, you don't stand a chance of being hired. And if you lie and they find out and hire you anyway, do you really want to work at a department like that? Your first thought was right on when you said you "will tell the complete truth about this." That's the way to go. No one is a saint. Feel bad about your actions, but never feel bad about having integrity.
In life's small things be resolute and great
To keep thy muscle trained: know'st thou when Fate
Thy measure takes, or when she'll say to thee,
"I find thee worthy; do this deed for me?"
Nemo me impune lacessit.