readonly in what sense. There's nothing such as read only in select tag. If you want to disallow user from changing the select tag's selected option, then you can disable it and enable it using javascript before the form is submitted...
As I said earlier, if you want to disable the select box, then you can use a javascript code to enable it back before the form submits. So on the onsubmit event of the form, you can enable the select box so that its value is also submitted when the form is submitted...