I would think it would depend on the situation. For the small stuff, it may be okay to use Equanimity. But if, for instance, that person's wrong perceptions may have consequences for you in the future, in that this person may go and tell someone else that you did such and such, and you didn't, it may actually damage your reputation in some way, then I believe it would be best to explain, in a nice way, that this is incorrect. Explain that you didn't do this particular thing that you are being blamed for. In all instances you have to use Equanimity, because if you get agitated and upset about this person blaming you because they believed another person's wrong perception, then you may not be able to convince this person that you didn't do it. So in all instances you have to use Equanimity, but you also have to use Compassion for yourself, understanding the repercussions of such blame if it is untrue, and learn how to stick to truth here. Because if you have a chance to correct something that is not true with this person, then they may actually stop the chain of gossip, or whatever this person is into, and telling others things that are wrong about you. However, there are situations where the other person is not actually confronting us about the incident. And we may not have the opportunity to actually explain to them, especially if they firmly believe in that, and they won't believe us anyway. So one also has to see whether it is within one's power to actually change this person's opinion.
If not then, Equanimity is more appropriate. And remembering Kamma, that I receives the results of my Kamma, if I didn't do it, then I do not receive the results of that action. The blame may be an opportunity to develop more Equanimity towards the eight worldly dhammas.