Firstly you do not necessarily have to study something relevant to Dentistry in Polytechnic to qualify for dental school in Singapore. I have a colleague who took Animal Science back in Polytechnic. However I would think it is preferably if your course was Science related. That said, as long as your GPA is good, and you have a strong CV and testimonial, you would also stand an equal chance in your dental school admissions.
Alternatively, if you are open to the idea of studying Dentistry overseas, you could consider countries like Australia and USA, which offers Dentistry as a post graduate study. Hence you would have to do an undergraduate degree first (preferably Sciences), and then apply for Dentistry thereafter.
You could check out this post on NUS dental school application that i have previously written for more details.
Hope this helps!
