Yosef Karo

“ And if one rented the house from an idolater, or rented the house to an idolater, one takes [the mezuzah] and leaves [with it when the lease expires] .
Rama: And an idolater who asks that one give her/him a mezuzah [because he/she] wants to affix it to his/her doorway, it is forbidden to give a mezuzah to the idolater. ”

“ All are obligated in [the performance of the mitzvah of] mezuzah, even women and slaves. And we teach children to perform [the mitzvah of] mezuzah for their doorways.
הכל חייבים במזוזה אפילו נשים ועבדים. ומחנכין את הקטנים לעשות מזוזה לפתחיהם. ”