Catechism of the Catholic Church §1301 — excerpt
The sign of peace that concludes the rite of the sacrament signifies and demonstrates ecclesial communion with the bishop and with all the faithful.
This translation is under copyright, so only the cited words are quoted here. Follow the link for the full text. Translation: English translation of the Catechism of the Catholic Church, 2nd ed. (Libreria Editrice Vaticana), as posted at vatican.va.
Also cites: St. Hippolytus, Trad. Ap. 21 SCh 11, 80-95