Don't sign anything.  That is what the union representative will tell you.  The manager can put refuse to sign on it.

But, you are not going to keep your job if your till is constantly short.

Never let anyone use your ID to ring up customers.  Never share a till with anyone.

I am not sure how the front end does it, but if two people share the same till, how can they tell who shorted the till?

How much was the till short? If it were short a few cents i don't think they would panic. But if its a subsantial amount, its bad. Especially if its constant. Signing a till shortage paper is not a guaranteed loss of job. Its a warning that you are being watched. Even if you refuse to sign, the till you are assigned to is linked to your checker number for the duration of your shift. So any shortages that happen while you are signed on is on you. Thats why you should sign off anytime you leave the register, carefully count money given to you by a customer, count change back, and NEVER share a till with ANYBODY, and do NOT give your password out to ANYONE.