Remove the javascript code from content placeholder and register it inside !Page.IsPOstBack. This will make it to render only when page loads for the first time.
protected void Page_Load(object sender, EventArgs e)
{
if (!Page.IsPostBack)
{
string jScript;
jScript="<script>print_country('ctl00_ContentPlaceHolder1_country', 'ctl00_ContentPlaceHolder1_state');</script>";
Page.RegisterClientScriptBlock("keyClientBlock",jScript);
}
}