When I did my police check, they required my ID and nothing else. Of course, I did it locally, so it wouldn’t have made sense to require a passport.
Yeah, you need your ID if you’re a citizen with HHR. For NWOHR, I’m sure you need your TARC, but you can always call and double check to see if they can make an exception if you don’t have yours on hand.
I still have my ARC from before I was granted citizenship so I might just apply with that and my ROC passport and see how I go
If it’s still not expired yet, then you might be able to send that to them with your other foreign passport, and they’d be none the wiser. 
Might not work if they communicate with the NIA though.
Just wondering if this is correct?
That’s what the instructions seem to say. It’s only $7 US so it should be fine.