Are you sure there isn't one stamped inside the electronics cavity?
I didn't know they had some of these without serials.
This is 100% correct - There are more than a few of the earliest NS2A basses (circa 1987 or so) that did not have serial numbers, I have one of them that I have owned since about 1988.

. Maybe I can buy a Dimension and hide it next to the water heater in the basement, she never goes there!!