Dropdown is a HTML Select equivalent. Just check the events exposed for a select and then use them as Attributes to add on server side.
Based on snippet above, all the three
methods[
^] should be there in dropdown too.
If in case you are talking of some button 'in' dropdown then you need to associate the JS after you find that control using Javascript. Use 'child' attribute if needed. You can use IE developer tool to see the complete HTML structure easily and then form the xpath to traverse and get the element needed.