R' Feinstein Igros Moshe 1959 Even HaEzer 1:Q56 (last paragraph); Even HaEzer 4:Q32, paragraph #9. For a translation of R' Moshe's three Teshuvos (responsa) on men shaking hands with women, see [4]
Nine to Five - A Guide to Modest Conduct for Today's Workplace by Rav Shmuel Neiman, p.14 (Safra 2001) ("[i]t has been rumored that Rabbi Moshe Feinstein, zt"l, ruled that it is permissible for men and women to shake hands. Nothing could be further from the truth! In his responsa, he agonized over this unacceptable practice and repeatedly stated that it is forbidden and infringes on giluy arayos" (emphasis in original)). This book has been criticized as containing many Chumros (stringencies not required by Halacha) that, while perhaps practiced in certain insular communities, are unrealistic to impose on all Frum (Orthodox) Jews in today's workplace; this opinion is shared by Rav Yehuda Henkin in the October 4, 2002 edition of Hatzofeh. See [5]. Cf. Rifka Schonfeld (March 2008): What Do I Say? What Should I Do? Challenges for the Ben Torah and Bas Yisroel in the Workplace, The Jewish Observer, p.17 (stating that there are "a number of excellent publications [about workplace interactions between men and women]", and that she recommends, in particular, Rabbi Neiman's Nine to Five - A Guide to Modest Conduct for Today's Workplace).