The need for the Chazan to say a few verses of scripture out loud before Kaddish of Musaf of Rosh Chodesh:
Background-When is the half Kaddish recited before Musaf: The Chabad custom, based on previous Poskim, is as follows: The Tefillin are to be removed after Uva Letziyon, prior to the half Kaddish recited before Musaf. The Tefillin of Rabbeinu Tam are also to be worn prior to the half Kaddish recited before Musaf. Consequently, according to the Chabad custom [and any other community who follows likewise], there ends up being a long break between the conclusion of Uva Letziyon and the recital of the half Kaddish, which creates the necessity of the law to be explained next.
The law: According to Chabad custom that the half Kaddish is recited right before Musaf, after finishing the wearing of Tefillin of Rabbeinu Tam, the Chazan is to recite a Psalm prior to reciting the half Kaddish before Musaf. This Psalm is to be concluded aloud for the congregation to hear. One is to recite at least three verses for this purpose; it is not necessary to recite an entire psalm. At least some of these verses are to be recited aloud. [This only applies in those communities that make a long break between Uva Letziyon and the recital of the half Kaddish before Musaf, as is the Chabad custom. However, those who recite the half Kaddish right after completing Uva Letziyon, or those communities who recite it right before Musaf but do not wear Rabbeinu Tam Tefillin, and immediately after removing their Rashi Tefillin begin the half Kaddish, have no need to recite verses of Scripture before saying the half Kaddish.]
 Admur 25:41; Siddur Admur; M”A 25:30; Elya Raba 25:25
The reason: The reason for this is because one needs to hear four Kedushas with his Tefillin and thus the Tefillin are worn until after one hears four Kedushas, as Barchu is also considered a Kedusha. [M”A 423:6]
Other opinions: Some Poskim rule the Tefillin are to be removed during Uvah Letziyon. [Peri Megadim, brought in M”B 423:10] The Custom of Chernobyl, based on a Kabala from the Maor Eiynayim in name of Eliyahu Hanavi, is to remove the Tefillin before Uva Letziyon.
 Siddur Admur; Elya Raba 25:25, brought in M”B 25:59; Ketzos Hashulchan 8:16 footnote 56; Os Chaim Veshalom 25:19; Igros Kodesh 2:50 [printed in Shulchan Menachem 2:195 and Shaareiy Halacha Uminhag 1:176]
The reason: The reason for this is because the half Kaddish relates to Musaf and by Musaf we do not wear Tefillin. [Rebbe ibid]
Other opinions: Some Poskim rule the Tefillin are to be removed after the Kaddish of before Musaf. [M”A 423:6; Arizal in Peri Eitz Chaim and Shaar Hakavanos, bought in Shaareiy Teshuvah 25:13 and Kaf Hachaim 25:94-95; Siddur Yaavetz] The reason for this is because one needs to hear four Kedushas and three Kaddishim with his Tefillin and thus the Tefillin are worn until after one hears three Kadeishim and one Kedusha. [M”A 423:6] However according to the Nussach of Admur that there are three Kaddeishim heard before Uva Letziyon, it is not necessary to wear the Tefillin during this Kaddish. [Ketzos Hashulchan 8 footnote 56; Rebbe ibid] See Background!
 Hayom Yom 1st Teves; Sefer Haminhagim p. 69 [English]; Kaf Hachaim 25:96; Os Chaim Veshalom 25:20; Toras Yekusiel 23; Chelek Halevi 21; Peri Hasadeh 2:97; Piskeiy Teshuvos 25:27
The reason: As the Kedusha of Rosh Chodesh is similar to the Os of Shabbos and Yom Tov and hence once Musaf is recited the Tefillin should no longer be worn. [Rashash in Nehar Shalom p. 14, brought in Kaf Hachaim 25:96]
 Igros Kodesh 20:283 [printed in Likkutei Sichos 19:485; Shulchan Menachem 2:201; Shaareiy Halacha Uminhag p. 177]; Sefer Hamamarim Likkut 2:316 of Rebbe Rayatz that so was the custom of the Rebbe Rashab; Luach Kolel Chabad; Nimukei Orach Chaim 55; See Admur 54:4; 292:4; See however Darkei Chaim Veshalom 64; M”B 25:59 in name of Elya Raba; Piskeiy Teshuvos 25 footnote 211; In 1988 the Rebbe directed the Chazan to recite a Mizmor prior to Kaddish of Musaf; Rabbi Leibal Groner confirmed with me that this is the practical custom that is followed and that the Rebbe directed to be done, and the Rebbe never retracted from his ruling. [This comes to exclude that which was said in Rabbi Groners name many years earlier that the Rebbe in the end retracted from his ruling. Rabbi Groner in his correspondence with us completely negated this as false]
 The reason: According to our custom to wear Rabbeinu Tam Tefillin before Musaf, we make an interval between Uvah Letziyon and the Kaddish said before Musaf. Therefore, a psalm needs to be said aloud before saying the Kaddish of before Musaf as Kaddish may only be recited after a passage of scripture. [Igros Kodesh ibid; Sefer Hamarim ibid; Nimukei Orach Chaim ibid; See Admur 54:4; 292:4]
 See Ketzos Hashulchan 16:2 and footnote 6; Ishei Yisrael 15 footnote 100; Custom of Rebbe and Chabad to recite the Mishnayos aloud after Davening; See Hiskashrus 601:19; Siddur Rav Raskin p. 483
Other opinions: Some Poskim rule it is not necessary to recite the Mizmor aloud. [Mateh Efraim 590:38]
 P”M 55 A”A 3 based on Kol Bo 6 and Darkei Moshe 54:1; Alef Hamagen 590:50; M”B 55:3 “A Mizmor or three verses”; Admur 54:4 “One is a to say a few Pesukim”; Admur 292:4 [one verse does not suffice to be an interval between Kaddeishim]; See Hiskashrus 460 p. 17
 Admur 54:4 “One is to teach them to say a few Pesukim between the Kaddeishim”
 As stated above from Poskim; Seemingly, one is not required to say all three verses aloud as is seen from the fact that we only conclude the last two verses of Ashrei aloud. However, see Ketzos Hashulchan ibid that implies that all three verses are to be said aloud, as one needs a Minyan who learns it.
 M”A 423:6; Arizal in Peri Eitz Chaim and Shaar Hakavanos, bought in Shaareiy Teshuvah 25:13 and Kaf Hachaim 25:94-95; Siddur Yaavetz
 Igros Kodesh 20:283 [printed in Likkutei Sichos 19:485; Shulchan Menachem 2:201; Shaareiy Halacha Uminhag p. 177]