refs is not a DOM element. In order to find a DOM element, you need to use findDOMNode menthod first.
Do, this
var node = ReactDOM.findDOMNode(this.refs.btn);
node.classList.toggle('btn-menu-open');
alternatively, you can use like this (almost actual code)
this.state.styleCondition = false;
you can then change styleCondition based on your state change conditions.