Try this:
First make AutoPostBack true Property in Drop_country Dropdown then
please write in page load :
if(!ispostback)
{
FillDropDownList();
}
------>
private void FillDropDownList()
{
DataSet ds = new DataSet();
SqlDataAdapter myda = new SqlDataAdapter("select Country from table name",connection object);
myda.Fill(ds);
drop_country.DataSource = ds;
drop_country.DataValueField = "Country";
drop_country.DataBind();
}
and double click on Drop_Country Dropdown
protected void drop_country_SelectedIndexChanged(object sender, EventArgs e)
{
DataSet ds = new DataSet();
SqlDataAdapter myda = new SqlDataAdapter("select state from table name where country='"+Drop_contry.Selecteditem.Value+"'",connection object);
myda.Fill(ds);
drop_state.DataSource = ds;
drop_state.DataValueField = "state";
drop_state.DataBind();
}
if any Doubt please post it....