Company X is a small ~50 employee money service business in the United States. Each employee is made to sign paperwork that says in the event an employee loses money in excess of $x.xx they're responsible for payment of the lost cash value as long as the error resulting in lost was made on their shift. If more than one employee working from the same cash in that shift results in loss and no one can determine whose at fault, we're made to come to some agreement to split the cost. This is the entire body of the agreement.

So some two weeks ago, it was found that some dollar amount was missing from any number of errors. This cash is counted at least once per week to maintain accuracy. At least 4-6 individuals regularly work with this cash. This week, those involved were informed that the fairest way to handle the situation is to split the loss evenly among all involved and pay it back, since they obviously were unable to pinpoint who did it or when.

Being said: is it right to want to refuse to make any restitution payment on money lost given the following? I'm not involved but I will refer to the individual in question as myself: 

1. I do not show on any reports handling the lost money;
2. There's no actual evidence of wrongdoing on my behalf otherwise;
3. My job is in handling compliance, but I am required to handle this money from time to time;
4. The management is basically saying because we can't implicate anyone specific, we'll simply punish everyone; and
5. This cash falls under the direct responsibility of someone other than me, and this person authorizes others to help out in handling the cash.

My question is, Am I right in refusing to want to pay this restitution money? And if they're adamant on their position, what are my options, does anyone recommend resigning? Cash lost is less than $500 USD, but this is on principle.

EDIT: This is pretty recent so we haven't gone into a meeting w/ management to discuss the matter in earnest, but I do want to have an idea of what sort of mindset I should be entering on i.e. i'm not just being overly difficult in my conviction and there's a tangible argument to the contrary.