My family had to establish a trust in order to protect my mother's house prior to her death. Now that she has passed away and the trustee has found a buyer for the house, do I need to worry about New York taxes (where the assets were located as well as the trust) as well as California taxes (where I live)? My entire distribution from the trust won't exceed $70,000.00

Given the size of the estate (unless you are one of 20 heirs), I suspect that you have NOTHING to worry about.

Most states follow the federal estate tax cutoff, which is $2 MILLION.

You can verify this by querying the state tax authorities for New York and California via their websites.