Related for Rosh Hashanah 1:11

[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.

The first of Elul is the beginning of the year for cattle tithing; R. Elazar and R. Shimon say: On the first in Tishrei. [Regarding this] Shimon b. Azzai said: Because some say "first in Elul" while others say “on the first in Tishrei”, the animals born in Elul are tithes for themselves. [What is that supposed to mean]? [Answer:] Five of them were born on Ab and five on Elul, five on Elul and five on Tishrei [or] five in Elul and five in Tishri, so they are not added together; [if he is] five [born] in Tishrei and five in Elul, behold, these are added together. '

Tishrei is the new year for the counting of the years, the shmita and the jubilees, for the planting of trees and for the greenery, for the tithes and the vows. How [one should understand]: for the years, the jubilee years, and the jubilee years? [Answer:] One counts [the months] for the years, the shmita and the jubilees only from Tishrei.

At the beginning of the year, all who have come into the world are passing before him [god] as a military unit; because it says: "He created their heart together" etc. And it says [further]: "Blow the horn on the new moon, at the full moon of our festival". And it says [further]: "For this is the statute of Israel, the law of the God of Jacob". Has the court sanctified the month, the process begins before him, and if the court has not done so, the process does not begin.

The ambassadors set out for six months. R. [Judah the Prince] ordered that they also will be sent for the Second Adar because of Purim.