Legal Question in Wills and Trusts in New Jersey

I'm not sure I understand the question. Responsibility for what?

-Tax liability?

-Providing date of death value to executor?

-Distribution as part of the estate under the will? Or is this account now treated as your property?

Was this an account merely used to pay bills, with the understanding that it was supposed to be part of the estate...subject to distribution under the Will?

If this was an accomodation account to allow you access to the account if your father was unable to access it himself, the proceeds are part of his estate, to go as his Will or the intestacy laws provide. If it was intended that he allow you to keep any balance, you have no responsibility to give the proceeds to his estate.