If you want to set a specific class name to the body tag in a page template, you can do something like this and do it dynamically:
<script runat="server">
protected void Page_Load(object sender, EventArgs e)
{
Page.DataBind();
CMS.DocumentEngine.DocumentContext.CurrentBodyClass += " your-class";
}
</script>
The class your-class
can also come from a property on that particular page type like so
CMS.DocumentEngine.DocumentContext.CurrentBodyClass += CurrentDocument.GetValue("ColumnName", "");