Didn't OP say that he only signed a contract at the end of his rental period? I have never rented a car outside of the US, but is it normal to require a signature when you return the car? What would be the repercussions of simply refusing to sign and leaving the car (with keys) with the drop off agent?

In the US, I never sign anything, either coming or going, when I rent from Avis, Hertz, or National. I just get my contract from the person at the exit and I usually don't even talk to the return person unless it happens to be a really slow time when I bring the car back.