Is it possible to do a research on both Computer Science and Law, without a Law Degree?
You most certainly can work in the intersection without a law degree, and a number of prominent people have done so.  A nice example is Edwina Rissland, who is a well-known expert on machine reasoning about the legal code, and who actually taught at Harvard law school for quite some time without ever having a law degree.  I heard one of her lectures on the subject once, and found it gave me a whole new understanding both about how our law really works and how we humans think about the world.

Do note, however, that without a law degree, you will likely need some collaborators who are lawyers, to help you with their expertise in the subject, just as if you were digging into computational chemistry without being a chemist yourself.  As for how to get into the area... just the same way as you would any other research area.