That's also an issue that generates a lot of controversy. It is really a matter of both the inherent aircraft stability and the perceived workload of flying the unaugmented aircraft in IMC. That establishes the hazard level of losing the autopilot function, which then dictates which power bus it gets put on.
Autopilots, themselves, are typically "non-essential" functions for IFR (typical for fixed wings), but for many helicopters, the autopilot system also provides the stability augmentation and attitude hold capability necessary to make the aircraft tame enough for IFR flight. (keeping the dirty side down).
In single pilot IFR, the pilot has to be able to take his attention away from the controls long enough to get an approach plate out or do similar tasks, without looking up to find that the world has inverted on him. Judging the un-augmented aircraft's tendancy to get to an unrecoverable or vertigo-inducing attitude is a very subjective thing, and there is very little guidance material on the subject. (How organized was the pilot before the failure, how far is the aircraft allowed to go with the hands off the controls for how long, etc.) It's really been a judgement call by the test pilot community and certification authorities. For DPIFR (Dual Pilot IFR), if the autopilot fails, its assumed that one pilot can be totally devoted to actively flying the aircraft, and so there are less issues involved.
In most of the twins I'm familiar with, the hazard level of would fall somewhere in the "Major" to "Hazardous" level. And that is why they typically have dual autopilot systems. I've been told the EC-135 has dual system with a third, limited back-up (I'm not sure what that says about the hazard level, since it's beyond what would typically be required for "hazardous", and less than what would qualify for "catastrophic." - or maybe I don't know enough about that system.
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As far as power goes, I can tell you that on the 412EP (same system as the S-76) that that the pilot's FCC is on the emergency bus. The co-pilot's is on the essential. But that's to preserve SAS and ATT hold capability. The flight director functions and coupled nav are all expendable.
Hope that answers you question.