Google 了一下有关法律，Child abuse

首先，几乎所有州和联邦都有相关法律

其中关于Physical Abuse部分：

Physical Abuse
Physical abuse is generally defined as "any nonaccidental physical injury to the child" and can include striking, kicking, burning, or biting the child, or any action that results in a physical impairment of the child. In approximately 38 States and American Samoa, Guam, the Northern Mariana Islands, Puerto Rico, and the Virgin Islands, the definition of abuse also includes acts or circumstances that threaten the child with harm or create a substantial risk of harm to the child's health or welfare.

在家打孩子，没有造成伤害，也没有人证，法律难以追究。但是如果有人证，即使当时看不出伤害程度，也会有人报警。