Siman 427

When Rosh Chodesh is two days – one begins to count the days of the month from the second day, except for Tishrei where the counting is from the first, because Elul is not intercalated. And that which we observe two days of Rosh Hashanah – this is because of Rosh Hashanah, as will be explained in its place. But for other months, when Rosh Chodesh is two days, the first day belongs to the past month, because of the reasons that were explained in siman 417. Therefore, the Tur and the Shulchan Aruch ruled here regarding legal documents, and in Even HaEzer siman 126 regarding gittin, that when writing a legal document or a get on the first day of Rosh Chodesh – one writes "on the first day of Rosh Chodesh of such-and-such [month], which is the thirtieth day of such-and-such past month." And regarding legal documents, there is no concern even to write ab initio "on the first day of Rosh Chodesh of such-and-such [month]," and no more. However, regarding a get there is more concern. And even there, ex post facto – it is valid. See what I wrote in Even HaEzer there.

When the year is intercalated, one writes for the first [month] "Adar" without qualification, as it is the primary [month] according to the opinion of most poskim. And for the second: "Adar Sheni." And if one wrote for the second without qualification – it is invalid. And so too when one recites the blessing for the month. Our teacher, the Rema, ruled accordingly. However, some are concerned according to what appears from the words of the Rambam in the tenth chapter of Nedarim, that the primary [month] is the second. Therefore, also for the first, one should write and announce "Adar Rishon," and such is the custom. But the primary law is: that the primary [month] is the first. And so one should conduct himself regarding the matter of yahrtzeit. And in Yoreh Deah siman 220 we elaborated on this, see there.