Just to be clear there could be three different sets of rights at work here.
Assuming that what you are saying is your own creation then you would be entitled to the copyright in the work itself - probably a literary work even if it wasn't actually written down - and you would also be entitled to the rights in your performance.
However you need to be entirely sure that the work which is overlaid on the greenscreen is genuinely free of copyright, or it has been released under an open licence (such as Creative Commons) which allows the creation of derivative works. If you intend to use something with a Creative Commons licence, check that it doesn't have 'ND' as its tag.
"Copyright in the video" is a slightly different matter. If you are the person who arranges for the making of the video then you would be entitled to the copyright in the video recording, but if the video was being made by someone else and was not necessarily being done under your direction, then it may be the person who is making the video is the owner of the copyright in it.
I hope this answers your question.