Painting over an old finish can be a difficult question. It depends on what the original finish was and what the new one is. Some paints, varnishes or lacquers will react badly with a previous coating. Others will just paint over with no problem.
If you can identify the finish, you may be able to get advice from people here who know more on the subject than I do. Otherwise, if you are talking an expensive instrument the two options are either "suck it and see" or strip the first finish and start afresh.
Quack!
Geoff the Duck.