Related for Rosh Hashanah 13:19
אמר רב יהודה אמר שמואל קרבנות צבור הבאין באחד בניסן מצוה להביא מן החדש ואם הביא מן הישן יצא אלא שחיסר מצוה
Has it not been taught: 'A leap year is not decreed<span class="x" onmousemove="('comment',' In the time of the Second Temple the calendar was not fixed, but the Beth din declared any year a leap year (i.e., inserted an intercalary month) according as they judged necessary, subject to certain rules.');"><sup>24</sup></span> before New Year,<span class="x" onmousemove="('comment',' Because if this were done, by the time Adar came round people might forget.');"><sup>25</sup></span>
Tosefta Rosh Hashanah (Lieberman)
[The month] Nisan is the beginning of the year for the kings, pilgrimage festivals, months, and the collection of the temple tax. Some say: Also for renting houses. How [one should understand]: "for the kings"? [Answer:] If he dies in Adar and another takes his place in Adar, the year is counted both for him and for the other. If he dies in Nisan and another takes his place in Nisan, the year is counted both for him and for the other. If [one] dies in Adar and another takes his place in Nisan, the first [year] is counted for the first and the second [year] for the second.
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Tosefta Shekalim (Lieberman)
All the congregational sacrifices are offered on the first of Nisan. And when the new moon comes in time, one sacrifice from the New, and if not, one sacrifice from the old. And if one offered [Pinge] for oneself, they were [as an offering] valid; only on the condition that they had to be handed over to the public.
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