Please refer this code

Put the Button in the Html code.

Filter Items (records) in ASP.Net DataList based on the selected value in DropDownList

HTML

<asp:DataList ID="dlCustomers" runat="server" RepeatLayout="Table" RepeatColumns="3"
    CellPadding="2" CellSpacing="2">
    <ItemTemplate>
        <table cellpadding="2" cellspacing="0" border="1" style="width: 200px; height: 100px;
            border: dashed 2px #04AFEF; background-color: #B0E2F5">
            <tr>
                <td>
                    <b><u><span class="name">
                        <%# Eval("ContactName") %></span></u></b>
                </td>
            </tr>
            <tr>
                <td>
                    <b>City: </b><span class="city">
                        <%# Eval("City") %></span><br />
                    <b>Postal Code: </b><span class="postal">
                        <%# Eval("PostalCode") %></span><br />
                    <b>Country: </b><span class="country">
                        <%# Eval("Country")%></span><br />
                    <b>Phone: </b><span class="phone">
                        <%# Eval("Phone")%></span><br />
                    <b>Fax: </b><span class="fax">
                        <%# Eval("Fax")%></span><br />
                </td>
            </tr>
        </table>
    </ItemTemplate>
</asp:DataList>
<br />
Country:
<asp:DropDownList ID="ddlCountry" runat="server">
    <asp:ListItem Text="All" Value="" />
    <asp:ListItem Text="Argentina" Value="Argentina" />
    <asp:ListItem Text="Belgium" Value="Belgium" />
    <asp:ListItem Text="Brazil" Value="Brazil" />
    <asp:ListItem Text="Canada" Value="Canada" />
</asp:DropDownList>
<br />
<asp:Button Text="Search" OnClick="SeachCustomers" runat="server" />

Namespaces

using System.Data;
using System.Data.SqlClient;
using System.Configuration;

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        this.PopulateCustomers();
    }
}

protected void SeachCustomers(object sender, EventArgs e)
{
    this.PopulateCustomers();
}

private void PopulateCustomers()
{
    string conString = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    string query = "SELECT top 10 * FROM Customers where Country=@Country or @Country=''";
    SqlCommand cmd = new SqlCommand(query);
    cmd.Parameters.AddWithValue("@Country", ddlCountry.SelectedItem.Value);
    using (SqlConnection con = new SqlConnection(conString))
    {
        using (SqlDataAdapter sda = new SqlDataAdapter())
        {
            cmd.Connection = con;
            sda.SelectCommand = cmd;
            using (DataSet ds = new DataSet())
            {
                sda.Fill(ds);
                dlCustomers.DataSource = ds;
                dlCustomers.DataBind();
            }
        }
    }
}

Screenshot