A. The general rule:
We do not say the confession prayer on Rosh Hashanah. Furthermore, some have the custom to omit the stanza of “Avinu Malkeinu Chatanu Lefanecha” from the Avinu Malkeinu prayer. This is done in order to avoid reciting confessions on Rosh Hashanah in order not to arouse the prosecutor. [Practically, we omit on Rosh Hashanah all stanzas that mention sin such as Chet or Avon and the like.] Similarly, we do not mention Tzidkascha when Rosh Hashanah falls on Shabbos in order not to arouse Divine judgment on a day of judgment.
The Chassidic explanation for why confession is omitted: On Rosh Hashanah we avoid mentioning the confession prayer. This is because the main focus of Rosh Hashanah is the coronation of G-d as our King, as it is on Rosh Hashanah that we accept the yoke of Heaven for the entire coming year. It is for this reason that no confession is made, as confession brings one to a state of remorse and broken heartedness which is a most unwanted atmosphere for the day of the Kings coronation. Rather we must rejoice over the acceptance of G-d to be our King. Now, although certainly one must also repent and have remorse on Rosh Hashanah, as how can there be a coronation if the nation is still in the midst of rebellion, nevertheless this is only a general remorse of one’s lack of discipline in following the Kings commands throughout the past year and a general re-acceptance of the Kings commands. It however is not remorse on each particular sin. A particular confession relates to Yom Kippur which is designated as the day of Teshuvah.
B. Confessing between Tekios:
See Halacha 13I for the full details of this matter!
Although we avoid confessing sins on Rosh Hashanah, and actually omit all mention of sin from the prayer Nussach, nonetheless in between the sets of blowing of Tashrat and Tahsat and Tashat and Tarat in the blows sounded before Musaf, it is an auspicious time to confess one’s sins. The confession is to be done in silent, and according to some Poskim is to be said in one’s mind without verbalization. The Chabad custom in this matter is inconclusive, with contradictory directives recorded in various sources. Practically, based on the talks of the Rebbe and Rebbe Rayatz one should at the very least recite a mental confession in his mind during this time, emphasizing a confession for the sake of Dveikus, attaching ones soul to G-d.
 Admur 584:2
 Beis Yosef 584; M”A 584:2 in name of Zohar; Arizal in Shaar Hakavanos 90a; Peri Eitz Chaim Shaar Rosh Hashanah 7; brought in Kaf Hachaim 582:16 and Kaf Hachaim 584:4
 Admur ibid; M”A 584:2; M”B 584:3
 Siddur Admur; Arizal in Shaar Hakavanos 90a; Peri Eitz Chaim Shaar Rosh Hashanah 7; Kaf Hachaim 582:16; Shaareiy Teshuvah 584:2
Ruling of Admur in 584: In 584:2-3 it seems that according to Admur only the stanza of Chatanu Lefanecha is omitted while Selach Umechal is recited. [In 584:2 Admur rules: “One needs to say Selach; Umechal; Mechei; Vihaver Chatoseinu Upeshaeinu as Mechila is greater than Selicha, and Pesha is greater than Chatas, and one must first ask for a minute matter and then add more.” Thus, it seems that even the second opinion in Admur held that sin can be mentioned in the stanzas on Rosh Hashanah. This applies also according to the M”A 584:3. Thus in total there are three customs in this matter: a) Recite everything [Rama] b) Only omit Chatanu. [Beis Yosef] c) Omit every mention of sin. [Arizal] See however Shaareiy Teshuvah 584:2, based on Kneses Hagedola, that those which omit the first stanza but recite the stanzas that contain the word sin are mistaken.
The reason: The Arizal ibid states based on the Zohar that on Rosh Hashanah one is not to mention any sin and hence one is to omit all the stanzas of sin, such as Mechol and Selach Lanu. [Kaf Hachaim ibid]
List of stanzas written by Admur in the Siddur that are to be omitted: “Avinu Malkeinu Chatanu Lefanecha”; “Avinu Malkeinu Selach Umechol Lechol Avonoseinu” “Avinu Malkeinu Michei Vehaver Peshaeinu Mineged Einecha” “Avinu Malkeinu Michok Birachamecha Harabim Kol Shitrei Chovoseinu”; “Avinu Malkeinu Kasveinu Besefer Selicha Umechila”.
 Admur 598:1
 Likkutei Sichos 9 p. 434; Igros Kodesh 22 p. 510