In LTA's regulations, they have classified modifications into
three categories:
(1) Allowed.
(2) Allowed only with approval from LTA - case to case basis.
(3) Disallowed.
From what I can see, gullwing doors are not specifically mentioned
in any of the above general guidelines (I've not seen the detailed
guidelines, if there are any). I suspect that gullwing doors may
come under category (2) above. LTA's general guidelines for car
modifications is
HERE.
Anyway, the main purpose of these LTA directives is to ensure
safety. And LTA has "question and answer" channel, via their
feedback website
HERE.
There are some cars with factory-fitted gullwing doors in
Singapore. One example is the Toyota Sera, pictures
HERE.
As for aftermarket gullwing doors, there are some workshops doing
it here too - and they do advertise it publicly. One example is
HERE.