The effect on power and range (which are not massive, perhaps 5 knots in Vmax, and perhaps 2% in range) will almost entirely be due to fuselage angle, with some contribution fom horizontal tail download, which looks to the rest of the helicopter like a weight gain. BTW, the range data that is published in the flight manual (if you are lucky enough to have some) is usually published at worst cg, so that it is conservative.
Aft CG: The nose is up more at Vmax, so the fuselage is pointed more squarely into the relative wind, for low cruise drag. Also, the horizontal tail is hardly working, its download is small, so generally the range is longest and the Vmax is highest. A negative for aft cg is that the rotor must be flapped down to get the high speed thrust, so the flapping could be a maximum, as would the shaft bending. These might cause shorter shaft life and therefore they might knock down the Vne a bit.
Neutral puts the nose down perhaps 3 degrees below aft cg, which could be below the neutral or at it. Usually there is little performance betwen neutral cg and aft cg, as a result. The forward flapping is better at high speed, however, so this could end up being the fastest speed.
Forward cg: The nose is down, so the fuselage is being towed thru the air with its broad top exposed to the free stream, making higher thrust, and this also creates a down load that looks like weight to the main rotor, adding to the misery. Usually the slowest point, and the worst for range, and the least comfort for the pax.