You can use a jQuery for validation on the dropdown list
jQuery.validator.addMethod("requireddropdown", function (value, element, params) {
var valid = false;
if ($(element).val() != params.defaultvalue)
valid = true;
return valid;
});
In code add this above the getter and setter of the DropDownList
[RequiredDropDown(ErrorMessage = "State is required.",DefaultValue="")]