Have you thought about the problem of acquiring two sets of Letters of Reference? It's often difficult enough to find three (or more) faculty who you are confident will write you a great letter. Are you going to ask each to write you two different letters, one saying you'll be up to the challenges of medical school and the other, dental school (such a request would not be appreciated and it will make you seem indecisive), or will you ask for a generic letter saying you'd be a great health professional (sorta tacky, and inviting the professor to comment on your indecisiveness in the body of the letter). Or, are you sure you can find six (or more) faculty to write separate, spectacular letters?
Personally, I think it's better for you to make up your mind before you ask for your LORs. Do some shadowing in both professions to help you decide.