Siman 84
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א מֶרְחָץ חָדָשׁ שֶׁלֹּא רָחֲצוּ בּוֹ, מֻתָּר לִקְרוֹת בּוֹ. וּבְיָשָׁן, בַּבַּיִת הַחִיצוֹן שֶׁכָּל הָעוֹמְדִים שָׁם לְבוּשִׁים, מֻתָּר. וּבָאֶמְצָעִי, שֶׁקְּצָת הָעוֹמְדִים שָׁם לְבוּשִׁים וּקְצָת עֲרֻמִּים, יֵשׁ שָׁם שְׁאֵלַת שָׁלוֹם, אֲבָל לֹא קְרִיאַת שְׁמַע וּתְפִלָּה: הַגָּה: וּמֻתָּר לְהַרְהֵר שָׁם בְּדִבְרֵי תּוֹרָה (רַ"ן פ"ק דְּשַׁבָּת וּפֶרֶק כָּל הַצְלָמִים) וּבַפְּנִימִי, שֶׁכֻּלָּם עוֹמְדִים שָׁם עֲרֻמִּים, אֲפִלּוּ שְׁאֵלַת שָׁלוֹם אָסוּר. וְאָסוּר לַעֲנוֹת אָמֵן בְּבֵית הַמֶּרְחָץ (רַ"ן פ' כירה):
1 Whether It is Permitted to Recite in the Bathhouse, containing 1 s'if A new bathhouse in which they have not washed - it is permitted to recite in it. And in an old [i.e. existing] one: in the outer room in which all who stand there are dressed, it is permitted, and in the middle room, where some who are standing there are dressed and some are standing there naked, one may greet another with the word "Shalom" (which is one of the names of God), but may not the recite the Sh'ma or the Prayer [i.e. Amidah]. Rema: and it is permitted to contemplate words of Torah there (Ran, Perek 1 of Shabbat and Perek "Kol haTz'lamim") And in the inner room where everyone is naked, even greeting others with the word "Shalom" is forbidden. And it is forbidden to respond "Amen" in a bathhouse (Ran, Perek Kirah)