I tried to look up your state's laws, but the website for all the laws is so horrible, I wanted to rip my eyeballs out.
The way it seems to work in most states is that turn signals are required for all motor vehicles, but a moped (or motorized bicycle, or motorized pedal-cycle, or whatever your state calls it) is specifically excluded from the definition of a motor vehicle. (Most states also have year requirements, like if it was manufactured before 19XX then you don't need them, although usually that's for motorcycles/motor vehicles, and usually we're outside of that definition anyway) . I did get far enough into the NJ laws to see that this does indeed hold true as a general definition for you -- mopeds are excluded from the definition of both a motor vehicle and a vehicle. However, I noticed in one of the later sections (for lighting) that the redefined "vehicle" just for that one section, and that definition DID include mopeds. You'd probably have to find the law that requires you to have turn signals (and if you got a ticket for it, the cop should have written it down), and then you can work on proving -- for current or future reference -- that he was right or wrong. That pdf above is probably a pretty good resource too, although it doesn't hurt to be able to cite the actual laws as well.