Publicly funded state institutions give preferential treatment to in-state applicants compared to those applying from out of state, some schools also have close relationships to residents of neighboring states but reciprocity exists to a much lesser degree than for undergraduate admissions. You would definitely need to check with the actual Admissions Office of the schools you were hoping to apply to though, as to how much preference there is, if there is at all. (For example, Ohio State, while publicly-funded, has about a 50/50 ratio of in-state to out-of-state matriculants).
Private medical schools rarely have an in-state preference though, but you'd need to verify this with their posted policies on their websites. This is why people generally apply to their in-state public medical school(s) and then solely to private institutions out-of-state, unless they have a really stellar application.