Does the parent of a child in catholic school in New York State have the absolute right to have the child transferred to another class?
And where can I find the rules or statutes pertaining to this?

A year late and a dollar short, but basically you work with the rules of the particular school your child attends. Parochial schools are not governed as public schools are. Personally, also in NYS, I would not send mychild to a non-public school unless I lived in a city (and even then it would be second thought about). Each employee and volunteer in a public school here needs to be fingerprinted (for the safety of the children) - that is not required in a private school; also in public, the teachers are required to be certified to teach that subject area, they do not even have to BE certified to teach in a private school. The person could be qualified to work at Burger King, but they can teach in a private school; they could be a pedophile from another area, and teach in a private school. Ridiculous. JMHO.