When you are in police custody for the first time in your life, you may realize how little you know about what happens next. You may also see that your very nature can be your downfall, especially when prosecutors are looking high and low for a criminal and your cooperation can be seen as a weakness that is more or less extrapolated on to a desire to put a pin in a case.
It is important to understand that while it may seem you have none of the rights and freedom to which you are accustomed, you do have some basic rights when it comes to self-incrimination and how guarded you must be with your own tongue, so as to not see your own words turned against you by the prosecution. Because if they can, they will.
Enter the Fifth Amendment, which does not go away because you are incarcerated. As soon as you are in police custody, and anything you say can be used toward your interrogation and proof of your guilt, someone must read you your Miranda Rights. These rights are simple, and you have likely heard them before on crime dramas. It is okay for you to not speak. It is okay to ask for an attorney, and you must have the aid of an attorney if you desire one, whether or not you can afford one. You must be reminded that what you say will be used to your detriment when possible. If you begin talking now and later decide you want an attorney, you must be granted an attorney. You also have the right to have your attorney present during any communication or interrogation by law enforcement, from the time you are taken into custody going forward.
It is worth mentioning that anything you said before you were taken into custody can still be used against you even though you were not yet read your rights. This is because you were not in the custody of the police, so a breakdown of your rights wasn't relevant yet.
When you are in a situation such as this, you would benefit from an attorney that is well-versed in the criminal justice system of the New York area and who can build a solid defense with you.