Some form elements can poke through floating divs that you might use for menus or whatever, as documented
here.
I had a problem with a select box so I made a DHTML control that works similarly. It's very minimally styled, but functional to work with other form elements.
This proof of concept has a text box so that you can see the value getting set. You'd change that to a hidden form element in real life.
See the select box
Dated: 12/30/2003