Is SearchString acting as property of Page class? Here is code,
<%@ Page Language="C#" %>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<script runat="server">
public string SearchString
{
get { return txtSearch.Text; }
}
</script>
<html xmlns="http://www.w3.org/1999/xhtml" >
<head id="Head1" runat="server">
<title>Button Search Typed</title>
</head>
<body>
<form id="form1" runat="server">
<div>
<asp:Label
id="lblSearch"
Text="Search:"
Runat="server" />
<asp:TextBox
id="txtSearch"
Runat="server" />
<asp:Button
id="btnSearch"
Text="Go!"
PostBackUrl="ButtonSearchResultsTyped.aspx"
Runat="server" />
</div>
</form>
</body>
</html>