With the code below I can do this procedure however I have to click the button. It looks like it needs a refresh to work
<asp:RadioButton ID="RadioButton1" runat="server" GroupName="pesquisa" /> Teste
<asp:RadioButton ID="RadioButton2" runat="server" GroupName="pesquisa"/> Teste2
<asp:TextBox ID="TextBox1" runat="server" Visible="false"></asp:TextBox>
<asp:Button ID="Button1" runat="server" Text="Button" />
C #:
if (RadioButton1.Checked == true)
{
TextBox1.Visible = true;
}