Okay, I googled and found this about NY law:
“Section 2164 of the Public Health Law permits the following two exemptions to this mandatory immunization requirement:
(1) If the parent objects to the immunization because the parent holds genuine and sincere religious beliefs which are contrary to the requirement that the child be immunized; or
Religious Exemptions
If you are seeking a religious exemption for your child, you must provide a written explanation of the foundations for your religious belief opposing immunization. In your own words, describe the religious principles that guide your objection to immunization. Also, indicate whether you are opposed to all immunizations, and if not, the religious basis that prohibits particular immunizations.”
So apparently I was only partially right as a parent can object but only on religious grounds. (In other words, simply being “smarter” than the accepted medical community is not sufficient.) If it’s due to medical reasons the letter must come from a doctor.