First, it's important to note that as a parent you are perfectly within your rights to refuse to let your children take this test; there is no legal consequences to you or your children by the state in doing so.
Every state is different, but in California, any parent can opt their child out of state testing by writing a letter (each year) to the school (check with your school district for specifics) and simply stating that they would like to opt their child out of state testing (name the test) for that academic school year.
Dear Principal Name, I wanted to let you know that my child, name, will not take part in the name the test this year. We ask that you make arrangements for him/her to have a productive educational experience during the testing period. Thank you for all you do.
Q: I have decided to opt my child out. What do I need to do? Write a letter or email to your principal letting them know that you intend to “refuse” the tests on behalf of your child. You can write your own letter or use our sample letter.