One who is reciting Tehillim and hears kaddish or kedushah from another room is not obligated to stop in order to respond.
Sources and Explanations
So emerges from the words of Rabbi Shlomo Zalman Auerbach zt”l in Halichot Shlomo (Tefillah, chapter 6, halacha 12), who wrote that if one hears kaddish or kedushah from another minyan, although he has the option to respond with them if he wishes, if this disturbs him from concentrating properly, and it is also evident that he is not counted as part of the other minyan, it is preferable that he not respond, but rather continue his tefillah. He proved this from the implication of the Shulchan Aruch (Orach Chaim 55:20), which writes, ‘even one who is not with them may respond,’ implying that he is not obligated to respond when he hears it from another minyan. In the notes they wrote that this was indeed the Rav’s practice: he did not respond to kaddish and kedushah even when he was at the beginning of the order of tefillah, reciting korbanot (the sacrificial passages) and the like. Similarly, it is cited in the name of Rabbi Yosef Shalom Elyashiv zt”l in the book Ashrei HaIsh (Orach Chaim vol. 1, chapter 10, halacha 13) that one who is passing in the street, or who is in his home, and hears a tzibbur responding to kaddish, kedushah, or Barechu, although there is no obligation to respond, it is good that he respond. In the notes they brought what is written in the pamphlet Alibba DeHilchata (issue 15), that he saw Rabbi Elyashiv many times, when he was going up to and down from the beit midrash and they would hear kaddish or kedushah from the central synagogue (the Shtiblach) of the Meah She’arim neighborhood, that he would not respond with them.
He explained there (halacha 12) that all the interruptions for answering kaddish, kedushah, and amen in the middle of tefillah, in the blessings of Shema, and the like, apply only if he is in the same room, but not in another room. And if he hears kaddish or kedushah while he is praying with another minyan that is in the same room, even if he is in the middle of Shema or its blessings, there is a mitzvah to respond, but there is no obligation to do so. Likewise, one who is learning and hears blessings or kedushah from the other room need not interrupt; but in the same room it is a disrespect if he does not respond, for if he does not respond he appears like a denier.
From the sefer “Shaf Veyativ – Laws of Saying Tehillim” by Rabbi Shay Tahan, Chapter 7: What Is Forbidden and Permitted When Saying Tehillim, Halacha 10 (p. 126 in the print edition). Translated from the Hebrew original.
