I have used the reference of the article ASP.Net AJAX AutoSuggest TextBox Example
For the AutoComplete, I have made use of OnClientItemSelected event for clearing the textbox
<div>
<asp:ScriptManager ID="ScriptManager1" runat="server" EnablePageMethods="true">
</asp:ScriptManager>
<asp:TextBox ID="txtContactsSearch" runat="server"></asp:TextBox>
<cc1:AutoCompleteExtender ServiceMethod="SearchCustomers" MinimumPrefixLength="2"
CompletionInterval="100" EnableCaching="false" CompletionSetCount="10" TargetControlID="txtContactsSearch"
ID="AutoCompleteExtender1" runat="server" FirstRowSelected="false" OnClientItemSelected="OnClientItemSelected">
</cc1:AutoCompleteExtender>
</div>
<script type="text/javascript">
function OnClientItemSelected(sender, args) {
$get("<%=txtContactsSearch.ClientID %>").value = "";
}
</script>