What is the ruling on giving Zakat to relatives when there is a state-affiliated Zakat board?

There is no objection to a person paying his Zakat to poor relatives whom he is not obligated to support; in fact, giving to relatives in such a case is better than giving to others.

If the just Imam establishes a Zakat office (Diwan al-Zakat), then if the wealth consists of cash or hidden assets, its owner is permitted to distribute it himself without dispute. If it consists of apparent assets (like livestock and crops), it is also permissible according to many scholars. So, a person who gives his Zakat to his poor relatives or to those eligible for Zakat, and whom he is not obligated to support, is not blameworthy, even if there is a Zakat office.