As a general rule, when there are two co-executors appointed, actions taken on behalf of the estate need to be taken by them jointly. The Letters issued to the two co-executors typically recite that they are the personal representatives acting together, and not either one of them acting alone. So when a bank account is opened, the account should be opened in the name of the duly authorized personal representatives, the two co-executors to whom Letters of Administration were issued.
As to "closing" an account, it may be that the two co-executors when they opened it, made checks payable for this particular account by either of them, for their administrative convenience. If they did so and the bank set it up that way, then one of them could draw down the account to zero by writing a check to empty the account. That would effectively close it or the bank might then close it after it had sat empty for a period of time.
The fact that there are two co-executors doesn't absolve either of them of co-responsibilities to the estate and duties to cooperate with one-another. If one of the two of them is the custodial and more active co-executor, he or she will be accountable to the other for disbursements and other actions.
If you believe one of the co-executors has overreached his office, you should review this with a local New Jersey probate lawyer, so that you may take appropriate action on a timely basis.