In NY it's legal to discipline (aka smack) your kids, in public or private, as long as it's open hand. So smack across the cheek or bottom is okay. Closed fist (aka punch) or using objects (belt, stick, etc) is not legal, even when in the privacy of your own home. A sheriff's deputy told me this because they'd get calls from teens wanting to report abuse, but when arriving on scene would explain to the child that the spanking or slap they got was perfectly legal.