Dunno about your law, but here home made phone recordings are admissable as evidence only if you had entered into agreement with law enforcement about it beforehand and if they are done in a preset way.
Other than that I too would suggest that you contact police/law enforcement about this case. Even if they will not be able to do much with the situation at hand, there might be other options available that you do not know about, plus they will explain you your legal rights and ways you can defend yourself both physically and legally. The more forces you have behind you in such a situation, the better.
I have had a death threat situation once, but I was absolutely sure when that happened that the person who did tell me those things would never actually come to any action, since that's what he was - a huge talker. Nevertheless I went to police just to form a protocol about the fact (he had sent me thinly veiled SMS messages), in case the situation developed in an unexpected way. Nothing more than talk never happened though, but I believe that the speak/do treshold varies greatly between people, so better be 10 times safe in this situation.