Navigate to id in Content widget from Text widget on Wordpress page

I have a Wordpress page with a text widget containing a select dropdown menu, along with a JQuery function to scroll to an id of a dl element in a separate content widget on the same page. The dl elements are contained within separate columns on a different widget. Here is my function:

<select id="select">
    <option value="">Select an option</option>
    <option value="londonderry">Amherst</option>
</select>
<script>
jQuery("#select").on('click', function() {
    alert(this.value);
    jQuery('html, body').animate({
        scrollTop: jQuery("#" + this.value).offset().top
    }, 2000);
});
</script>

As content is spread over multiple columns, I just can't place the dropdown menu in one of the columns; placing the code in the header of the widget with the columns wraps it in paragraph tags. Any ideas on why this is not working?