Is it illegal to put an 11-year-old in a choke hold?

First of all, "refusing to talk" is not an offense that many people would object to, but even so, many people would consider a choke hold at least over-reaction and perhaps at most, child abuse. Many people would also say that using violence such as this is both psychologically and physiologically harmful to the child. You need to make a more enlightened decision about whether refusing to speak is one that merits discipline and then secondly, I would suggest you find a better means of discipline perhaps "time-out," no dessert, grounded etc. This is dangerous and harmful. Don't do it.