In NYS, changing schools will not decrease your taxes. The only way to accomplish this is to move physically to a different district with a lower tax rate.
If you retain your current place of residence and send your child to another school you risk the likelyhood of paying school taxes on the property where you live plus tuition for the new school.
Do look into NCLB regulations. Also do not hesitate to contact the New York State Department of Education for a clarification if necessary.
The "Eckler Team"
Michael Saunders & Company