Mr. Gold and Mr. Zelinger give you good advice. If you are referring to a bank account (or an account at any financial institution, and if your mother is the only name listed on the account, then the only option would be to file a probate proceeding (if there is a will) or an administration proceeding (if there is no will), unless it is a small estate, in which case a simplified proceeding known as "voluntary administration" can be done.
Let me raise one other important point. Your posting states that you are in New York City. That's all well and good, and as fine a place as any other for you to be, but is entirely irrelevant. The real question is where your mom resided at the time that she passed away.
A probate or administration proceeding is done in the county in which the decedent resided at the time of her death; and if she did not reside in New York State, then an "ancillary" proceeding must be done in any state in which assets are located. If your mother lived out-of-state, and the asset had a NY situs, then such a proceeding must be done if, after careful examination, an attorney determines that the type of account at issue is one that could be considered as being located in NY.
You would do well to retain an experienced estate attorney. Most probate and administration proceedings are not expensive, particularly those that (a) are not contested; (b) are modest in value; (c) don't involve complicated issues, such as locating lost-lost relatives who may be entitled to notificaton of the proceeding.
Good luck to you.
Michael S. Haber is a New York attorney. As such, his responses to posted inquiries, such as the one above, are limited to his understanding of law in the jurisdiction in which he practices and not to any other jurisdiction. In addition, no response to any posted inquiry should be deemed to constitute legal advice, nor to constitute the existence of an attorney/client or other contractual or fiduciary relationship, inasmuch as rendering legal advice involves the ability of the attorney to ask appropriate questions of the person seeking such advice and to thus gather appropriate information. In addition, an attorney/client relationship is formed only by specific agreement. The purpose of this answer is to provide the questioner with general information, not to outline specific legal rights and remedies.
You don't say which type of account or where she is...But if an account is owned by just the deceased person it would stand to reason that it is an estate item (probate item). You also do not say if you are the only child or if there is a spouse. If there is no spouse, children would be the heirs at law, unless she had a will in which case the will would say who the beneficiaries are. If you need to open probate it would be in the county where she resided at death.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature.
You cannot change the beneficiary on her account. It now falls into the "estate" and will be dealt with at the Surrogate's court. Depending on whether your mother left a Will or whether she was married and/or had other children, will help determine the outcome. There are too many variables missing from your question to really advise.
I may be guessing or not licensed in your state. No atty/client relationship exists.