Set title attribute for ListItem in DropDownList if you do not want tooltip then don't add title attribute.
<asp:dropdownlist id="ddlNoOfMonths" runat="server">
<asp:listitem text="select1" value="item1" title="tooltip"></asp:listitem>
<asp:listitem text="select2" value="item2"></asp:listitem>
</asp:dropdownlist>
using C# code.
for (int d = 0; d < DropDownListControlName.Items.Count; d++)
{
DropDownListControlName.Items[d].Attributes.Add("title", DropDownListControlName.Items[d].Text);
}