As a follow up to this question: (6 Tevet 5763 Kaparat Pasha on Rosh Chodesh Rabbi Aaron Adler) In every Siddur I’ve ever seen or used, the only instruction given for "Ul’chaparat Pasha" is "say this on leap year only". Never have I seen in any Siddur that it is only said until Adar II. Why is this instruction not given, if it is the way it is done all over?
There are different customs. The Mishnah Berurah (323, 6) notes that some say Ul’chaparat Pesha (for atonement of sin) on every Rosh Chodesh (beginning of the month) all the years, not only in a leap year. Some say it in a leap year until the end of the year. Others say it only in a leap year and only until the end of the leap month that is the second month of Adar. In all of these customs “Every river runs its own course” and everyone shall follow the custom of his place. I briefly checked a few Siddurim (prayer books) and found that in those of the Jerusalem publishers Eshkol and Miller, they actually do note that it is for a leap year until Rosh Chodesh Nissan, but as we noted this is just one of the customs.