Commentary for Avodah Zarah 41:2

Although in the previous mishnah we learned that in certain places it is permitted to let a house to an idolater (in Syria according to Rabbi Meir, and in the land of Israel according to Rabbi Yose), this permission is not granted if the idolater is renting the house as a residence. Since the idolater will bring his idols into the house, this would violate the prohibition of allowing idols into one’s home. The idolater may only rent the house from the Jew to use for storage or other non-residential usage. [The Jerusalem Talmud rules that outside of the land of Israel it is permitted to sell or let houses to idolaters even for the purpose of residence. Although in this case too the idolater will bring idols into the house and seemingly thereby cause the Jew to violate the commandment in Deut. 7:26, the essential meaning of the verse is that it is forbidden for a Jew to bring idols into his own house. The halacha is more strict inside the land of Israel and in bordering areas because it is incumbent upon Jews to cleanse the land of idol worship.]

In no place, even outside the land of Israel, may one let a bath-house to an idolater. Since the bath-house will continue to be called by the name of the Jewish owner, and the idolater will surely bring idols into the warehouse, this is forbidden.