Every state is different and I believe dental schools follow the same rules colleges do in determining state residency and that has to do with many factors. The main one is Intention, which is basically what you are doing in that state. Some states have a strict Intention rule which says that if you only go to that state to be educated you do not qualify for instate tuition. So year after year you end up paying out of state tuition because you never spent a year in that state doing something besides going to school. Another factor is dependency, where if your parents are providing tons of support for you and they live in another state you may not qualify (I know dependency for FAFSA is irrelevant for dental students but FAFSA and Residency have different qualifications, although I could be wrong). But if you take out loans for yourself you are considered independent.
So read up on the state laws for residency determining those factors and the rest should be universal, which is that you must have lived at least a year in that state, filed income taxes for that state, registered to vote in that state, registered your tags for that state, etc.