You need a permit and electrical inspection; the last thing you want is the fire department marking you have non-permitted electrical work if something happens. Depending on your setup you may need both a rough and final inspection if you need to go behind drywall. We just needed a final because we used exterior conduit. What exactly you ask for will totally depend on your current setup and where you want the wall connector mounted. In most cases, you’ll just need an electrical permit. Our town counted it as adding an outlet because there isn’t a sub category on the common permit app for EV “Appliance” yet. Talk to your town’s building department and they’ll walk you through what they want from you. For us it was described on the permit as “Electrical alteration: installation of Tesla Wall Connector outlet and associated wiring.”
A ton of EVs are out on the road in CNJ. Pretty much every town from Clinton Township to Crawford has a lot of experience with these types of permits now. If you have an existing subpanel like we do, the inspector will primarily check you have the correct gauge wire (must be at least 6 awg because the WC is “capable” of drawing 60 amp), correct breaker for the commissioned setting on the wall connector (so 30 amp, 40 amp, etc), and it appears to turn on and function properly. You don’t actually need your EV yet. Inspection took 5 min for us.