If I don't agree with the performance appraisal, should I sign it?
If you disagree with the performance evaluation your manager has completed about you, you can, and probably should sign it. Usually, forms used to today's organizations require that you sign the form, but your signature simply acknowledges that you have read the evaluation (or discussed it with your manager), not that you agree with it.
If asked to sign a performance evaluation form with which you do not agree, check to see what you are signing. Does it say something like "I acknowledge that I have read this form"? If so, when you sign it you indicate only that you have read it, not that you agree with it.
If the form clearly indicates you are simply acknowledging that you have read it, refusing to sign it is probably not in your best interests. It's a meaningless gesture, if you are doing it simply out of spite or frustration.