I would like to know if a employee has to pay back money shortages
from their till if one or more managers have been in their till and if
they are aloud to suspend you if you refuse to pay back the money.
Even if you haven't signed a piece of paper stating that you have to
pay back till shortages.

I believe the laws differ from state to state, but in California, if
memory serves, they cannot withhold anything from your paycheck
without your consent (unless ordered to do so by the court, such as a
garnishment).

Usually, there is only on cashier allows in the register.  This is for
control and accountability purposes.  Therefore, if you were the only
one on the register and the count is short, its your fault and the
appropriate disciplinary action up to and including dismal can be
taken.  If others were ringing up sales during the same period you
were in the register, there is no conclusive proof it was you (unless,
of course a survelance camera caught you on tape giving $5 change when
it should have been $50).  Video is hard to dispute.

You mention inventory shortages in your title, but not in your
question.  What is the situation.  Perhaps I can offer an opinion.

Signed,

Ex-corporate controller, retailer chain of 300 store.