Burlesque literally means to ‘parody’ but don’t forget that a parody is very different to straight imitation or copying. A parody must contain direct referencing of the intended subject and make a new point or original comment. A direct imitation or copy of something historical differs greatly from something current.
Imitating or copying something from the past, is typically done in ‘homage to’ or in respect of the original artist and their work. If it is a parody then it is done with a sense of humour, pointing out flaws or obscurities. Performers intending to do either, should be sure that they do justice (and give credit) to their original source of inspiration. A weak copy is anything but a tribute. A cruel parody can be anything but funny.
Imitating or copying anything which is recognized as a signature act of a current performer is generally felt to be taboo and should be avoided. Copying a modern day performer’s act could also lead to an infringement of their performing rights and lead in to legal issues surrounding their persona and intellectual property. Don’t forget, successful performers have worked hard in carving out their niche and rely on their image and signature pieces for their own income.
However, if a certain signature act is so well known that it invites parody or satire, then playful use of the routine is generally acceptable providing the intention of the parody is clear, is justified and that the original artist is given due credit. If in any doubt about the suitability of borrowing an idea from another artist, contact them before making any advance to ensure that you will not be treading on any toes.