Ref:
Display No results found message (No match found message) in jQuery AutoComplete
Please refer this code
HTML
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <script src="http://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.10.0.min.js" type="text/javascript"></script>
    <script src="http://ajax.aspnetcdn.com/ajax/jquery.ui/1.9.2/jquery-ui.min.js" type="text/javascript"></script>
    <link href="http://ajax.aspnetcdn.com/ajax/jquery.ui/1.9.2/themes/blitzer/jquery-ui.css"
        rel="Stylesheet" type="text/css" />
    <script type="text/javascript">
        $(function () {
            $("[id*=txtSearch]").autocomplete({
                source: function (request, response) {
                    $.ajax({
                        url: 'Default.aspx/GetAutoCompleteData',
                        data: "{ 'username': '" + request.term + "'}",
                        dataType: "json",
                        type: "POST",
                        contentType: "application/json; charset=utf-8",
                        success: function (data) {
                            if (data.d.length > 0) {
                                response($.map(data.d, function (item) {
                                    return {
                                        label: item.split('-')[0],
                                        val: item.split('-')[1]
                                    };
                                }))
                            } else {
                                response([{ label: 'No results found.', val: -1}]);
                            }
                        }
                    });
                },
                select: function (e, u) {
                    if (u.item.val == -1) {
                        return false;
                    }
                }
            });
            $("[id*=txtSearch1]").autocomplete({
                source: function (request, response) {
                    $.ajax({
                        url: 'Default.aspx/GetAutoCompleteData1',
                        data: "{ 'username1': '" + request.term + "'}",
                        dataType: "json",
                        type: "POST",
                        contentType: "application/json; charset=utf-8",
                        success: function (data) {
                            if (data.d.length > 0) {
                                response($.map(data.d, function (item) {
                                    return {
                                        label: item.split('-')[0],
                                        val: item.split('-')[1]
                                    };
                                }))
                            } else {
                                response([{ label: 'No results found.', val: -1}]);
                            }
                        }
                    });
                },
                select: function (e, u) {
                    if (u.item.val == -1) {
                        return false;
                    }
                }
            });
        });
    </script>
</head>
<body>
    <form id="form1" runat="server">
    <div>
        <div class="span12">
            <input type="text" id="txtSearch" />
            <input type="text" id="txtSearch1" />
            <button type="submit" style="margin-top: -11px;" class="btn btn-warning btn-large">
                Search
            </button>
        </div>
    </div>
    </form>
</body>
</html>
Namespaces
using System.Data.SqlClient;
using System.Web.Services;
using System.Configuration;
 C#
[WebMethod]
[System.Web.Script.Services.ScriptMethod()]
public static List<string> GetAutoCompleteData(string username)
{
    List<string> result = new List<string>();
    using (SqlConnection con = new SqlConnection(ConfigurationManager.ConnectionStrings["Constr"].ConnectionString))
    {
        using (SqlCommand cmd = new SqlCommand("select  ContactName from Customers where ContactName LIKE '%'+@SearchText+'%'", con))
        {
            con.Open();
            cmd.Parameters.AddWithValue("@SearchText", username);
            SqlDataReader dr = cmd.ExecuteReader();
            while (dr.Read())
            {
                result.Add(dr["ContactName"].ToString());
            }
            return result;
        }
    }
}
[WebMethod]
[System.Web.Script.Services.ScriptMethod()]
public static List<string> GetAutoCompleteData1(string username1)
{
    List<string> result = new List<string>();
    using (SqlConnection con = new SqlConnection(ConfigurationManager.ConnectionStrings["Constr"].ConnectionString))
    {
        using (SqlCommand cmd = new SqlCommand("select  ContactName from Customers where ContactName LIKE '%'+@SearchText+'%'", con))
        {
            con.Open();
            cmd.Parameters.AddWithValue("@SearchText", username1);
            SqlDataReader dr = cmd.ExecuteReader();
            while (dr.Read())
            {
                result.Add(dr["ContactName"].ToString());
            }
            return result;
        }
    }
}