Well, if you're never going to show it to anyone else, you might theoretically need the rights, but in reality no-one is likely to care. If you're making it for your film school and film festivals, you can often negotiate a cheap rights deal which will only allow it to be shown in such situations; if you then, say, had a TV company want to show your short you'd need to renegotiate the rights. Any serious festivals will normally want proof that you have rights to the music before they show your movie.
Personally I always found it too much hassle and got a composer to create original music.