Nefilas Apayim in an area without a Sefer Torah:
A. The general law:
Some [i.e. Ashkenazim, and some Sephardim] are accustomed to only perform Nefilas Apayim [i.e. the resting of one’s face towards one’s arm] in an area that contains a Torah scroll. [If the area contains a Torah scroll, then one may perform Nefilas Apayim even if there isn’t an Aron for the Torah scroll in the room, and even if it is not in a shul, but rather inside the privacy of one’s home.] In an area without a Torah scroll, they are accustomed to reciting [all of the parts of] Tachanun, although without covering their face [i.e. performing Nefilas Apayim].
Other Opinions and customs:
Some Poskim argue on the entire law above and rule that one may perform Nefilas Apayim even in an area in which a Torah scroll is not found. Practically, one who is lenient in this and performs Nefilas Apayim even when Davening alone at home, has upon whom to rely, and so is the custom of Jerusalem Jewry. However, those who are accustomed like the first opinion to not perform Nefilas Apayim unless there is a Sefer Torah present, are not to change from their custom, and a new Rav does not have ability to make them change, and so is the custom of Ashkenazim, and some Sephardim, as stated above.
The Chabad custom & the custom of the Rebbe:
The ruling of the Alter Rebbe, to which the Chabad custom should remain faithful to, is not to perform Nefilas Apayim in an area that does not contain a Torah scroll, even if it contains other Torah books, and so indeed is the widespread custom of world Jewry in general, including Chabad Chassidim. Nonetheless, some members of Anash are accustomed to perform Nefilas Apayim even when a Sefer Torah is not present based on an acclaimed testimony that so was done by the Rebbe. On the other hand, however, we find clear testimony in the diaries of Rabbi Groner to the contrary that the Rebbe did not perform Nefilas Apayim in an area that did not contain a Torah scroll. Possibly, one can answer the contradicting testimonies by stating that in those areas that the Rebbe performed Nefilas Apayim is because it was done at the same time as the Minyan, in which case even according to the above stringency one may perform Nefilas Apayim, as stated in C. Practically, the original ruling of the Alter Rebbe is to be upheld as there is not enough evidence to the contrary to say that the Chabad custom is any different. Nonetheless, those who follow the other opinion are not to be protested as stated above.
 See Admur 131:3; Kaf Hachaim 131:40-50; Piskeiy Teshuvos 131:10-12; Halacha Berurah [Yosef] 131:
 Admur ibid; Rama 131:2 “Some Poskim rule that one may only perform Nefilas Apayim in an area that contains an Aron and a Sefer Torah…and so is the custom”; Rokeiach 324; Beis Yosef 131 in name of Rokeiach; Taz 131:4; Rameh Mipuno Asara Mamaros Chikur Din 1:23; Ketzos Hashulchan 24:4
The opinion of Kabbalah: Some Poskim rule that according to Kabbalah, one may perform Nefilas Apayim even in an area without a Sefer Torah. [Birkeiy Yosef 131:1; Siddur Arizal Rashkov; Kaf Hachaim 131:40, however, see there that he concludes that in truth, so long as one says all the section of Tachnaun, and simply omits performing Nefilas Apayim, it is valid even according to Kabbalah, as one is not losing out on any part of the prayer; See Nimukei Orach Chaim 131]
 Admur ibid in new print of Shulchan Aruch, based on first printing, however, in previous prints it simply states that “The custom is…” without the word “some”’; Rama ibid “Some opinions rule.. and so is the custom”
Other opinions: See below!
 Rama ibid
 Shiyurei Kneses Hagedola 131:4, brought in Kaf Hachaim 131:40 that so is the Ashkenazi custom, and the custom of some Sephardic communities; However, see Birkeiy Yosef 131:1 that the Sephardic custom is like the Michaber, to perform Nefilas Apayim even in an area without a Sefer Torah; Kaf Hachaim 131:40 concludes that each community is to follow his custom
 Must the area also contain an Aron? The Rama ibid writes that it is to contain both an Aron and a Sefer Torah. Seemingly, this is based on the verse brought next which explicitly states the term “Aron Hashem.” However, Admur omits this requirement completely. This follows the ruling of the Taz ibid who writes that there is no need at all for there to be an Aron in the room, and simply having a Torah scroll in the room suffices, “and the words of the Rama are not to be taken literally, and so is written in the Rokeiach as recorded in the Beis Yosef”
 Implication of Admur ibid who omits “Aron”; Taz ibid; Elya Raba 131:5; Beir Heiytiv 131:6; Soles Belula 1315; M”B 131:11; Kaf Hachaim 131:44; See previous footnote!
 M”A 131:6 that so is proven from the story in the Talmud with Rebbe Elazar; Beir Heiytiv 131:6; Ateres Zedkeinim 131; M”B 131:11; See Levushei Serud 131:6
 Shiyurei Kneses Hagedola 131:4; Kaf Hachaim 131:40 and 46 that based on Arizal one is to say all the parts, including: Yud Gimel Midos [if there is a Minyan], the Mizmor of Nefilas Apayim [i.e. Ledavid Eilecha Hashem Nafshi] but without performing Nefilas Apayim; Divrei Yatziv 1:74
 Admur ibid; Rama ibid; Shut Maharil 72; Minhagei Maharil Tefila p. 445
The reason: A hint to this matter can be found in Scripture regarding the war over the city of Aiy, in which the verse [Yehoshua 7:6] states “Vayipol Al Panav Lifnei Aron Hashem/and he fell to his face before the ark of G-d.” [Admur ibid; Taz ibid; Rokeiach ibid; Beis Yosef ibid; M”B 131:11] From this it is learned that one should only fall on his face and perform Nefilas Apayim if he is in front of the ark of G-d which refers to the Torah scroll.
 Shiyurei Kneses Hagedola 131:4 in name of Rav Avraham Galiko that one may do Nefilas Apayim even in an area without a Sefer Torah, and in an area that is not a Shul, brought in Kaf Hachaim 131:40; Shiyurei Kneses Hagedola 131:4 and Birkeiy Yosef 131:1, brought in Kaf Hachaim 131:40, that so is the ruling according to Michaber; See Beis Yosef ibid “I say [regarding the ruling of the Rokeiach ibid] that if it is a tradition then I accept it. If, however, it is a novel ruling based on the verse, then I have an answer which can refute it.” See Taz ibid that the answer to refute the proof from the verse in Scripture is that there is another area in Scripture regarding Pilegesh Bigivah in which it states that they repented in front of G-d, and just like in that verse regarding repentance nobody will say that you can only repent if you are in front of the Torah scroll so too nobody should learn from our verse here that you can only perform Nefilas Apayim if there is a Torah scroll present; Taz ibid that so is implied to be the opinion of the Rosh that there is no need to have a Torah scroll present; Birkeiy Yosef ibid in name of Maharamit, and that so applies according to Kabbalah; Shiyurei Bracha 131:1 in name of Mahram Milameid in Mishpat Tzedek 3:19 that one who looks into the words of the Poskim will see that they all argue on the Rokeiach, as seen from Setimyas Divreihem; Kesher Gudal 19:16; Shalmei Tzibur p. 150; Beis Oveid 1; Chesed Lealafim 131:12; Siddur Arizal of Rav Shabsi Miroshkav; Kaf Hachaim 131:40 that so applies according to Kabbalah, although concludes that each community is to follow his custom; Luach Eretz Yisrael Tukichinsky and Ketzos Hashulchan 24:4 that so is Minhag Yerushalayim, as Jerusalem is considered to always be in front of G-d
 Birkeiy Yosef 131:10 that this applies both according to Halacha and Kabbalah; Shiyurei Kneses Hagedola 131:4, brought in Kaf Hachaim 131:40; Shalmei Tzibur p. 150; Beis Oveid; Kaf Hachaim 131:41; Nimukei Orach Chaim 131
 Ketzos Hashulchan 24:4; Luach Eretz Yisrael Tukichinsky; Rav SZ”A in Ishei Yisrael 25 footnote 39 [however, see there that this only applies in the old city]; Teshuvos Vehanhagos 2:79 [regarding old city]; Igros Moshe 3:129 [See there that those who visit Jerusalem are to follow this custom and perform Nefilas Apayim even when praying at home]
The reason: As Jerusalem is always considered to be in front of G-d, in front of the Aron. [Luach Tukichinsky]
 See Mishpat Tzedek 3; Kneses Hagedola 131; Birkeiy Yosef in Shiyurei Bracha 131:2; Shalmei Tzibur p. 150; Beis Oveid 2; Kaf Hachaim 131:42
 See Admur 131:3; Ketzos Hashulchan 24:4; Hiskashrus 164 p. 15; Hearos Ubiurim Ohalei Torah Gilyon 1201, article of Rav Baruch Oberlander, p. 56
 So plainly rules Ketzos Hashulchan 24:4
 So is written in Hiskashrus ibid in the name of Rav Groner, and so I was told by Rav Groner in a personal correspondence that indeed he witnessed the Rebbe performing Nefilas Apayim in rooms that a Torah scroll was not present, such as occurred one time when the Rebbe Davened Mincha in a printing house on his return from the Ohel, and that so occurred many times when the Rebbe Davened in a private minyan in the Gan Eden Hatachton. Accordingly, those who question whether Rabbi Groner ever made such statements and are not sure of anyone who actually heard from him, can rest assured that he did make such statements, as he affirmed to us personally in written correspondence.
 Sefer Hamazkir Vol. 1 pp. 104-105 from the personal diary of Rabbi Groner which was written decades before his acclaimed testimony based on his memory, and there he writes that when the Rebbe was in the printing house he did not perform Nefilas Apayim, and did not even sit down for the saying of Ledavid Eilecha Nafshi Esa, even though a chair was prepared for him to do so.
 As aside for the fact that we see that there is contradictory testimony regarding the Rebbe’s custom [from the same individual!], and the fact that we can explain that when the Rebbe was seen to perform Nefilas Apayim it was due to the fact it was praying at the same time as the Minyan, furthermore, even if it were clear that the custom of the Rebbe is unlike Admur, it is not clear that this should be followed by the public. This is especially due to the fact that regarding Nefilas Apayim we find a special status given to great Torah scholars and leaders. [See Admur 131:1] We indeed asked Rabbi Groner, who is the source behind the testimony of the Rebbe to having seen him perform Nefilas Apayim, as to whether this is a directive for the public, he stated to us that perhaps it can be interpreted as a directive for the public, but he himself was not completely sure.