I actually found a way to do so.
                                        <tr>
                                            <td>
                                                <b>State:</b>
                                            </td>
                                            <asp:Panel runat="server" ID="pnllbls" Visible="true">
                                                <td>
                                                <asp:TextBox ID="txtstate" runat="server" MaxLength="200" Width="250px" ReadOnly="true"></asp:TextBox>
                                                </td>
                                            </asp:Panel>
                                            
                                            
                                            <asp:Panel runat="server" ID="pnlstate" Visible="false">
                                              <td>  
                                                    <asp:DropDownList ID="State" runat="server" class="form-control input-lg" DataSourceID="SqlDataSource1" DataTextField="State"
                                                        DataValueField="SId" OnSelectedIndexChanged="State_SelectedIndexChanged" AutoPostBack="true" AppendDataBoundItems="true">
                                                        <asp:ListItem Value="0">--Select--</asp:ListItem>
                                                    </asp:DropDownList><br />
                                                    <asp:SqlDataSource ID="SqlDataSource1" runat="server" ConnectionString="<%$ ConnectionStrings:ConnectionString %>"
                                                        SelectCommand="SELECT DISTINCT SId,State FROM [State]"></asp:SqlDataSource>
                                                </td>
                                            </asp:Panel>
                                            
                                        </tr>
                                        <tr>
                                            <td>
                                                <b>City:</b>
                                            </td>
                                            <asp:Panel runat="server" ID="pnllblc" Visible="true">
                                             <td>
                                                <asp:TextBox ID="txtcity" runat="server" MaxLength="200" Width="250px" ReadOnly="true"></asp:TextBox>
                                            </td>
                                            </asp:Panel>
                                            <asp:Panel runat="server" ID="pnlcity" Visible="false">
                                                <td>
                                                    <asp:DropDownList ID="city" runat="server" class="form-control input-lg" DataSourceID="SqlDataSource2"
                                                        DataTextField="City" DataValueField="Id" AutoPostBack="true" AppendDataBoundItems="false">
                                                        <asp:ListItem Value="0">--Select City--</asp:ListItem>
                                                    </asp:DropDownList>
                                                    <asp:SqlDataSource ID="SqlDataSource2" runat="server" ConnectionString="<%$ ConnectionStrings:ConnectionString %>"
                                                        SelectCommand="SELECT DISTINCT [Id], [City] FROM [City] WHERE ([SId] = @SId)">
                                                        <SelectParameters>
                                                            <asp:SessionParameter Name="SId" SessionField="sid" Type="Int32" />
                                                        </SelectParameters>
                                                    </asp:SqlDataSource>
                                                </td>
                                            </asp:Panel>                                          
                                        </tr>
                                        <tr>                                          
                                            <asp:Panel runat="server" ID="pnlbtn">
                                                <td colspan="2" align="center">
                                                    <asp:Button ID="btnchange" runat="server" Text="Edit" CssClass="btn btn-info" OnClick="btnstate_Click" Width="50px" Height="30px" />
                                                </td>
                                            </asp:Panel>
                                        </tr>
                                        <tr>
 
            if (!IsPostBack)
            {
                mycon.Close();
                mycon.Open();
                cmd.Connection = mycon;
                cmd.CommandType = CommandType.Text;
                cmd.CommandText = "Select City,State,phone,Contact_person,Address,Company_website from Company_profile where email='" + Session["mail"].ToString() + "'";
                SqlDataReader dr = cmd.ExecuteReader();
                if (dr.HasRows)
                {
                    while (dr.Read())
                    {                        
                        txtstate.Text = dr["State"].ToString();
                        txtcity.Text = dr["City"].ToString();
                        txt_no.Text = dr["phone"].ToString();
                        txt_Contact.Text = dr["Contact_person"].ToString();
                        txt_address.Text = dr["Address"].ToString();
                        weblink.Text = dr["Company_website"].ToString();
                        btnsave.Visible = false;
                        btnUpdate.Visible = true;
                    }
                }
            }
 
        protected void btnstate_Click(object sender, EventArgs e)
        {
            pnlcity.Visible = true;
            pnlstate.Visible = true;
            pnllbls.Visible = false;
            pnllblc.Visible = false;
            pnlbtn.Visible = false;
        }