The director of health shall also return all nonresident public charges admitted to or hospitalized at the hospital to the states in which they may have a legal residence. For the purpose of facilitating the return of such persons, the director may enter into reciprocal agreements with the proper boards, commissions, or officers of other states for the mutual exchange of such public charges whose legal residence is in another state, and the director may file written permission for the return of any residents of the State now confined in a public institution in another state, corresponding to any institution coming within the definition of state hospitals for the insane, or in which they were under detention, not having been lawfully discharged therefrom.