New York State law provides at section 11-0512 of the Environmental Conservation Law that “No person shall knowingly possess, harbor,… any wild animal for use as a pet in New York State, except as provided in subdivision three of this section.” Subdivision three provides that “Any person who possesses or harbors a wild animal for use as a pet at the time that this section takes effect may retain possession of such animal for the remainder of its life…”  The law took effect January 1, 2005. There are additional exceptions to the ban, including, for example, exhibitors licensed pursuant to the federal Animal Welfare Act and licensed wildlife rehabilitators. The law provides requirements in the law for those allowed to keep wild animals, such as getting a permit and complying with rules and regulations. “Wild animal,” as defined in section 11-0103, includes (among other species) “Felidae and all hybrids thereof, with the exception of the species Felis catus (domesticated and feral cats, which shall mean domesticated cats that were formerly owned and that have been abandoned and that are no longer socialized, as well as offspring of such cats) and hybrids of Felis catus that are registered by the American Cat Fanciers Association or the International Cat Association provided that such cats be without any wild felid parentage for a minimum of five generations…” Local laws may be even more stringent. You should consult with an attorney in your area to discuss next steps.

I don’t know why a neighbor would call the police if you curb your dog, clean up after your dog, and dispose of the feces in accordance with the law unless there is an order of protection or some other issue not mentioned in your question.  Of course, those other issues could affect what actions the police may take. Generally, as long as one complies with the canine waste and littering laws in their localities, they will not be fined for violating these laws. I suggest you contact your town clerk or town attorney to get a copy of the canine waste and littering laws in your area.