Access attributes of asp.net controls from JQuery
<asp:TextBox CssClass="myclass" ID="Name" runat="server" ToolTip="some tooltip">/asp:TextBox>

$(document).ready(function() {
        $('.myclass').click(function() {
                alert($(this).attr('ToolTip'));
           });
});

alert($(this).attr("title"));

$(function () {
        $('.mybutton').onclick(function () {
            var tooltip = "B";
            $('.mytb').attr('title', tooltip);
        });
    });

  <button type="button" CssClass="mybutton">Click Me!</button>
  <asp:TextBox ID="TextBox1" runat="server" ToolTip="A" CssClass="mytb"></asp:TextBox>