Open Question: What happens to a joint CD bank account when one person dies?

My grandmother and I have a shared CD account. The money is mine, but I wanted someone else to be on the account to avoid questions. My grandmother has an estate planned so that her money is distributed amongst her children. My question is, if she dies will the money still go to her estate, or will it be just under my name since I was also on the account? If it's a factor, I live in Massachusetts.