What does a bank need if a deceased person has certificate of deposit or accounts in their bank?

They actually don't need anything. However if someone needs to withdraw the money from that account of the deceased person they must:

1. provide proof that the person is actually deceased (A death certificate)
2. provide proof that he/she is the legal heir of the deceased (A will or a relationship proof that they are the son/husband/wife/daughter of the deceased)

Once the bank verifies these documents, they will release the funds from the deceased persons accounts to you. Without these you cannot take any money from that account.