To purchase this Sefer, click here
Tachanun is omitted on Rosh Chodesh.
Tzidkasecha: When Rosh Chodesh falls on Shabbos, Tzidkasecha is not recited during the Mincha prayer.
Hitting the chest during Selach Lanu: One does not hit his chest during the blessing of Selach Lanu said during Shemoneh Esrei of Rosh Chodesh, and the same applies on any day in which Tachanun is omitted.
Kerias Shema Sheal Hamita: On the night of Rosh Chodesh the Viduiy prayer is omitted from the bedtime Shema, although one does recite the Ribono Shel Olam. On Motzei Rosh Chodesh one recites the regular bedtime Shema including the Viduiy prayer.
 Siddur Admur; Hashlama of Rebbe Nechemia 131/8
 Admur 292/7; Siddur Admur
 Siddur Yaavetz in name of Shlah; Sefer Haminhagim p. 139 [English]; Ishkavta Derebbe footnote 33 that so was the custom of the Rebbe Rashab
 Hayom Yom 28th Adara 1; Sefer Haminhagim p. 49 [English]
 Sichas Pesach Sheinyni 1983 12 [printed in Toras Menachem 1983 3/1414] “On Motzei Rosh Chodesh there is not enough of a reason to exempt the recital of Tachanun, being that the second day of the month has already begun”