I would say no. However, that wont stop the nursing home from asking. Gather the paperwork you ha e and see a consumer or elder lawyer to get more precise advice
I am not licensed in NY, so you will have to go to an attorney in your jurisdiction should you need formal help. However, it is very unlikely that they can go after you for the bills unless you specifically signed something stating you would be responsible. I also believe there is a federal regulation against this practice as a condition of admission to a facility if that facility accepts Medicare. I would write “DECEASED - NO ASSETS” in big marker across a recent bill and send it back to them and see if that stops collection efforts.
Generally speaking, the surviving relatives are not responsible without signing an agreement which would make you responsible. The nursing home is not allowed to condition admission to the home upon such an agreement. Despite these limitations, nursing homes routinely and increasingly are coming up with clever attempts to hold the surviving relatives responsible. If they do this to you, speak with a consumer attorney.
Unless you have co-signed for her payment obligations, you will not be liable for her debts. I'm sorry to hear about your loss.
Good luck with your case!