Q. I have noticed that some Chassidim give a brocho to others of Chasima Tova o Gemar Tov (good ending) on the last day of Chanuka, as we usually do in Hoshana Rabba? Is this actually correct and why?
A. Toldos Aharon (Drushim Lechanuka) based on the Mishna Bikurim (1: 6) (See also Pesachim 36b) which teaches: that from Atzeret (Shavuos) until the Festival (of Sukkos), one brings Bikurim and recites the corresponding ordained declaration. From Sukkos until Hannuka, one brings Bikurim but does not recite anything. This establishes that there are two very distinct periods of Judgment. One ends in Hoshana Rabba while the other finishes at the end of Chanuka.
They also quote Talmud Yerushalmi (Shabbos 2: 6) as well as Tur Barekes (581), on the posuk 'Hanosen Bayam Derech,' that the yearly days of Judgment last until the end of Chanuka. They mention that the writing of the verdict of the year's trials is given on Rosh Hashana, then the signature is done on Yom Kippur. Yet the giving over of the Judgment sentences takes place only later on Hoshana Rabba, however, the very delivery and enactment of those sentences does not take effect until the end of Chanuka.
That is why it is still proper to bless others with Chasima Tova or Gemar Tov at the end of Chanuka. (Nitei Gavriel 56: 1)
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit'a