With the exception of one reference (Ex 12:2) the New Year is never specifically dated. The religious calendar apparently began in the spring and the agricultural calendar in the autumn. Later Judaism began its calendar in the autumn.
Evidence that the autumn was regarded as the New Year
The dedication of Solomon's temple
1 Kings 8:2Solomon waited 11 months after the completion of the temple (see 1Ki 6:38), before dedicating it, most likely because the great Feast of Tabernacles marked the beginning of the year.
Instructions for celebrating the Year of Jubilee
Leviticus 25:8-9The Year of Jubilee was to be proclaimed on the tenth day of the seventh month, which was also the Day of Atonement.See alsoLeviticus 16:29
Ezekiel's vision of the new temple
Ezekiel 40:1This vision of the new temple takes place at the beginning of the year. The “tenth of the month” refers presumably to the seventh month.
Jeroboam's institution of an autumnal festival
1 Kings 12:32This autumn festival was clearly intended to be equivalent not only to the feast in Judah, but also to other pagan New Year festivals, in spite of the eighth month being distinctive.See also1 Kings 12:33
Evidence that the spring was regarded as the New Year