We hold our cash count slips for three months. They are rpinted daily (our software cannot maintain them), and them verified and proofed by the closer in charge.
The only reason that we maintin them is that once in a great while, something pops up from the backroom showing that the teller possibly did not balance afterall, so it is a nice go to for us to have to see what the cash count was that day.
Keep in mind, the tellers do always realize what goes on behind the scenes, and do not realize the value of the slips. I would confer with your supervisors, and backroom support, and see if and how they would use them. If they have no use for the slips, and the branch staffs cannot see a point for them either, then perhaps it is time to try a change!
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I don't repeat gossip, so listen closely...