Use the onChange event of thr drop_category and use the selectedIndex to find if its the selected item.
drop_category.Attributes.Add("onChange", "newCate();");
in the code behind and in the js
function newCate() {
var e = document.getElementById('ctl00_<panelname>_drop_category');
if (e.options[e.selectedIndex].value == '0')
window.open('Category_Manage.aspx', null, 'height=250, width=250,status= no, resizable= no, scrollbars=no, toolbar=no,location=no,menubar=no ');
return false;
}
Replace the value with whatever value you have. Do Note that your control name in javascript may be different. If you have your javascript as inline you can use the ClientId to retrieve the drop down's name when it is rendered in html. Like this:
document.getElementById('<%= this.drop_category.ClientID %>');