In Ohio, a speeding ticket received for 1 to 5 miles per hour over the posted speed limit is 0 points according to the OH points system. It is also 0 points in Ohio for a speeding citation of going 6 to 10 mph over the posted speed limit if the speed limit is 55 mph or above.

In New Jersey a moving violation for 1 to 14 mph over the speed limit is 2 points. So if you received the ticket in NJ you would be assessed 2 points. Also, as you stated New Jersey assigns 2 points for moving violations received out of state and ensures the violation also becomes part of your driving record.

The NJ Motor Vehicle Comission's site states that the 2 points are given for out of state violations and does not note any exceptions such as if the ticket would result in 0 points in the state in which it was received or if the state in which you were cited does not have a points system. From that I would take that 2 points are assigned across the board. To verify this you can contact the NJ MVC.