The film makers made quite a bit of effort to disguise the real location, more than is warranted, I feel, but here are a few examples...A few red herrings here because, yes, there is a place called Central Hospital, but it's not this place. Secondly, there is the Chinese name 中央醫院 (Jung Yeung Yi Yuen), which is the original name of a venue now known as the Sai Ying Pun Jockey Club Polyclinic, and no, it's not that place either.
Then there is another red herring in the form of an address we see at one point (when Marenta - played by Robert Taylor - heads off to do some investigation on the 'Middle Man'). We see a hospital invoice. Check out the address below. It says 222 Waterloo Road.
This, coincidentally (or not, as I suspect is the case) is the actual address of the Baptist Hospital in Kowloon Tong. Hmmm.
So, why these guys went to so much trouble I don't know. But either way, it has had me scratching my head until I was doing some research on another matter (as is usually the case) and I discovered some great pictures on FLICKR of the old British Military Hospital on Wylie Road in King's Park.
Here's the ink: https://flic.kr/p/8CAhHr.
A wiki entry can also be found here:
Anyway, suffice to say, the other major reason I had so much difficulty is because this building has been replaced by a huge apartment complex called Parc Palais. You can read a bit more on wiki but the upshot is that the hospital was decommissioned on 30th June 1996 and eventually demolished in the early 00's before Parc Palais was built (opened in 2004).