<div class="main">
	<div class="lpanel">
		<input type="radio" onclick="changes(this);" name="shipping_method" id="shipping_method_local_delivery" value="local_delivery" />
		<label for="shipping_method_local_delivery">Местная доставка</label>
		<input type="radio" onclick="changes(this);" name="shipping_method" id="shipping_method_local_pickup" value="local_pickup" /> 
		<label for="shipping_method_local_pickup">Самовывоз (Бесплатно!)</label>   
	</div>
	<div class="rpanel">
		<input id="shiptobilling-checkbox" class="input-checkbox" type="checkbox" name="shiptobilling" value="1" />
	</div>
</div>

<script>
	window.onload=function changes(element) {
			var sel = document.getElementById("shiptobilling-checkbox"),
				radio = document.getElementsByName("shipping_method");
			if(element.value == "local_pickup") {
				 sel.document.getElementById('shiptobilling-checkbox').checked = true;
			} else {
				sel.document.getElementById('shiptobilling-checkbox').checked = false;
			}
	}
</script>

function changes(element) {
    document.getElementById('shiptobilling-checkbox').checked = (element.value == 'local_pickup') ? true : false;
}