it depends
if the household puts it up so he & his children can look at the tzaddik as a role model & hope to learn from his ways then it can be hanging in his home or office
on the other hand if it is a rebba or mekubal etc… that is looked at or viewed/treated like a g-d/avoda zara then it cannot be hanging in his house.
i.e. if you need someone to turn to or depend on then turn to Hashem for help. who is there more of a chance of being answered, Hashem straight or a messenger of Hashem