Thr rules say if you win and have 0 buildings you must shut it down. But you can't shut that section down.
No they don't. The relevant rule section is here on page 8:
Note: a player may choose to build fewer skyscrapers than he is allowed (even
none!).This means that a player may participate in an auction even when he has
no skyscrapers in his supply. If no player bids in an auction, that district is skipped
and the auction for the next district begins.
What you are referencing is the procedure for when a district is already full. In this case, you have two options: 1) Place more skyscrapers (but only if you have a district already) or 2) Don't place any skyscrapers (because you choose not to or because you don't already own a district).
If you choose (2) then the Stop mechanic takes effect.
The key here is that the district has to be full in order for this to take effect ("When all building plots in a district have skyscrapers or businesses on them before the auction..."). Since Central Park can never be full (("each player may build any number of skyscrapers (based on his bids) in the area below Central Park")), this would never apply to Central Park anyway.