Snowman doesn't process the tags of a Passage (current or others) so you will need to use JavaScript to look at the Passage's tw-passagedata element, which is a child of the tw-storydata element that stores the definitions of all the passages.
The following example shows how to use jQuery to first obtain the relevant tw-passagedata element based on the Passage's name, and then how to use the attr() function to obtain the String value that contains the assigned tag names (each separated by space character).
var passage = $('tw-storydata tw-passagedata[name="Name-of-Passage"]');
var tags = passage.attr('tags');
console.log('tags: ' + tags);