Financial Web notes that to close a joint bank account, one or both of the account holders must go to the bank in person and request to close the account. The bank may require the account holder to show photo identification and sign a formal request to close the joint account. Once the bank's terms are met, the account is closed and remaining funds are distributed to the account holder.
According to Daily Finance, some banks require the consent of both account holders to close a joint account. The bank may accept signed paperwork from one account holder if both cannot be present when the account is closed. Some banks require both parties to be present at the branch location where the account was opened in order to close it. Because each person has equal ownership of the funds and is allowed to make changes to the account, the bank may require only one account holder's consent to terminate the joint account.
About.com notes that before either party on a joint account decides to terminate it, both parties must discontinue using the account and wait for all pending transactions to clear before closing it. This includes stopping all automatic drafts and deposits to the account. Once the account is closed, both account holders should receive a letter from the bank noting that the account has been terminated.