Where I work, we all have access to the petty cash box which is kept in a locked drawer. Sometimes we sell things (exam books, tickets to events that we sponsor) and we all can handle those transactions. There are about 8 people with access to the cash box. No one person is responsible. We’d all be questioned if there was a discrepancy but it doesn’t occur to any of us, I guess, because in the over 4 years that I’ve been here, that has not happened.
If you are concerned, request a meeting with your supervisor or with whomever told you that you are solely responsible. Ask them how you can be held responsible when the other person has access too. I am betting there’s a perfectly reasonable explanation, or that you are mistaken about being solely responsible. Perhaps the paperwork you signed that you are responsible was from years ago and now it’s changed because the new guy is added on. Clarify it with the boss.
If your meeting still doesn’t pan out to your satisfaction, send an email with your concerns. The good thing about email is that it’s got a time and date stamp on it and it can be as clear as you want it to be. That way, nobody can say that the discussion didn’t take place and there should be no misunderstandings.