1. Add a Button with OnClick event. Set its style property as Style = "display:none" so that it is hidden.
 
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4/jquery.min.js" type="text/javascript"></script>
    <script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8/jquery-ui.min.js"
        type="text/javascript"></script>
    <link href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8/themes/base/jquery-ui.css"
        rel="Stylesheet" type="text/css" />
    <script type="text/javascript">
        $(document).ready(function () {
            $("[id*=txtSearch]").autocomplete({
                source: function (request, response) {
                    $.ajax({
                        url: '<%=ResolveUrl("~/Service.asmx/GetCustomers") %>',
                        data: "{ 'prefix': '" + request.term + "'}",
                        dataType: "json",
                        type: "POST",
                        contentType: "application/json; charset=utf-8",
                        success: function (data) {
                            response($.map(data.d, function (item) {
                                return {
                                    label: item.split('-')[0],
                                    val: item.split('-')[1]
                                }
                            }))
                        },
                        error: function (response) {
                            alert(response.responseText);
                        },
                        failure: function (response) {
                            alert(response.responseText);
                        }
                    });
                },
                select: function (e, i) {
                    $("[id*=hfCustomerId]", $(e.target).closest("td")).val(i.item.val);
                    $("[id*=btnSubmit]").click();
                },
                minLength: 1
            });
        }); 
    </script>
</head>
<body>
    <form id="form1" runat="server">
    <asp:TextBox ID="txtSearch" runat="server"></asp:TextBox>
    <asp:HiddenField ID="hfCustomerId" runat="server" />
    <br />
    <asp:Button ID="btnSubmit" runat="server" Style="display: none" Text="Submit" OnClick="Submit" />
    </form>
</body>
</html>
 
    protected void Submit(object sender, EventArgs e)
    {
        string customerName = Request.Form[txtSearch.UniqueID];
        string customerId = Request.Form[hfCustomerId.UniqueID];
        //Get the details from database here
    }