Not that I am aware of. I know a few states allow conjugal visits, North Carolina not being one of those states.
The above is not intended as legal advice. The response does not constitute the creation of an attorney-client relationship.
Inasmuch as constitutional rights are largely taken away from those convicted of crime, the state does not have to allow interaction between men and women. There are undoubtedly female employees at men's prisons and male employees at women's prisons. If by interact you are referring to conjugal visits, that has already been answered.
R. Jason de Groot, Esq.,