You can use given sample code to adding tooltip to DropDownList. you need to just adding Title attribute to the list item in DataBound event.
<asp:dropdownlist id="DropDownList1" runat="server" ondatabound="DropDownList1_DataBound" xmlns:asp="#unknown">
</asp:dropdownlist>
and Now below code in Code behind file
protected void DropDownList1_DataBound(object sender, EventArgs e)
{
DropDownList ddl = sender as DropDownList;
if (ddl != null)
{
foreach (ListItem li in ddl.Items)
{
li.Attributes["title"] = li.Text;
}
}
}