I don't know what inverter
you have but RCD's do not necessarily work reliably on the output of an inverter
due to harmonics. Many inverter manufacturers provide lists of RCD's they have tested on their inverters.
Quasi sinusoidal inverters are obviously the more problematical but I would not blindly rely on a sine wave one either as I have known harmonic sensitive equipment
to fail on them too.
We elected to not have one on the output of our own inverter (quasi-sinusoidal) as the risk inside our boat is extremely low (the engine
and all internal metal fittings apart from the propellor shaft are isolated from AC earth). But as we have a metal boat I am careful on the rare occasion that I use power tools powered from it on deck
as I have found portable RCD's also to be either obviously unreliable or not trustworthy.
I haven't checked but I think in recent times ABYC, if one intends following it, requires an RCD on inverters - Gord or someone could probably clarify that if it has not already been so in this thread. ISO requires a 30mA RCD on the "main power supply" which one assumes to mean on each power supply and so on an inverter, but gives the alternative option of using 10mA RCD's on all receptacles in the galley
, bathroom, machinery space and weather deck
instead (for those spaces we only have receptacles in the galley). As always the standard should be itself checked in order to be sure if intending to rely on this advice.