It is legitimate... after it has been migrated to the site that holds the dupe-question. If a question is a duplicate of a question on another site, a true duplicate with identical content from the same user, then a judgment call needs to be made about which site is the question more appropriate for and then move the off-topic question to the right site for dupe-close.
For near-dupes, identical concepts but different words and users, it is far from clear cut. If the topic is one that resides in the overlap between here and there, then it could quite happily live here; there is a preference site-wide to keep questions on their original site unless it needs to move. It could also be a dupe of a ServerFault question. If it is a near-dupe, there is no ServerFault question it could be a dupe of, and is topically gray, drop an Off Topic close vote on it. When the question gets migrated, vote for dupe-close or flag on the target site.
Because of the above, we have no method of handling cross-site duplicates and cross-posts. Cross-posts are the one case where we'd like to have this ability, near-dupes nearly always fail the 'topical' test as well as dupe.