Using reference from my article, I managed to do it
And the plugin from https://twitter.github.io/typeahead.js/examples/
Database
Install the Northwind and Pubs Sample Databases in SQL Server Express
HTML
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
    <script type="text/javascript" src="http://twitter.github.io/typeahead.js/releases/latest/typeahead.bundle.js"></script>
    <link rel = "Stylesheet" href = "https://twitter.github.io/typeahead.js/css/examples.css"></link>
    <script type="text/javascript">
        $(function () {
            $('#the-basics .typeahead').typeahead({
                hint: true,
                highlight: true,
                minLength: 1
            },
            {
                name: 'states',
                displayKey: 'value',
                source: function (request, response) {
                    $.ajax({
                        url: '<%=ResolveUrl("~/Default.aspx/GetCustomers") %>',
                        data: "{ 'prefix': '" + request + "'}",
                        dataType: "json",
                        type: "POST",
                        contentType: "application/json; charset=utf-8",
                        success: function (data) {
                            response($.map(data.d, function (item) {
                                return {
                                    value: item.split('-')[0],
                                    id: item.split('-')[1]
                                }
                            }))
                        },
                        error: function (response) {
                            alert(response.responseText);
                        },
                        failure: function (response) {
                            alert(response.responseText);
                        }
                    });
                }
            });
        });
    </script>
</head>
<body>
    <form id="form1" runat="server">
    <div>
        <div id="the-basics">
            <input class="typeahead" type="text" placeholder="Northwind Customers" />
        </div>
    </div>
    </form>
</body>
</html>
Namespaces
using System.Data;
using System.Web.Services;
using System.Configuration;
using System.Data.SqlClient;
using System.Web.Script.Services;
Code
[WebMethod]
[ScriptMethod(ResponseFormat = ResponseFormat.Json)]
public static string[] GetCustomers(string prefix)
{
    List<string> customers = new List<string>();
    using (SqlConnection conn = new SqlConnection())
    {
        conn.ConnectionString = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        using (SqlCommand cmd = new SqlCommand())
        {
            cmd.CommandText = "select ContactName, CustomerId from Customers where " +
            "ContactName like @SearchText + '%'";
            cmd.Parameters.AddWithValue("@SearchText", prefix);
            cmd.Connection = conn;
            conn.Open();
            using (SqlDataReader sdr = cmd.ExecuteReader())
            {
                while (sdr.Read())
                {
                    customers.Add(string.Format("{0}-{1}", sdr["ContactName"], sdr["CustomerId"]));
                }
            }
            conn.Close();
        }
        return customers.ToArray();
    }
}
Screenshot
