In the State of Minnesota where hunting deer with dogs is prohibited, the law states:
Any hunter may and any conservation officer must attempt to kill any dog seen chasing a deer during the deer-gun hunting season". Most dog owners lock their dog up during the season.

Here in Nebraska it's legal to use dogs to hunt deer although I've never seen anyone do it.

If we see a dog harassing any wildlife here and it has no collar (hense no proof of vacination) we practice the SSS rule...(shoot,shovel,and shutup)