Light Yagami's interactions with the police in the anime "Death Note" are significant because they showcase his intelligence, cunning nature, and ability to manipulate those around him. These interactions also highlight the cat-and-mouse game between Light and the authorities, particularly L and the task force, as they try to uncover his identity as the infamous Kira. Additionally, Light's interactions with the police serve to demonstrate the moral ambiguity of his actions and the ethical dilemmas faced by both law enforcement and society in dealing with a vigilante who takes justice into his own hands.