TT #44 · Parshas Tazria · Aliyah 1 · Passuk 6
English: On the completion of her period of purification, for either son or daughter, she shall bring to the priest, at the entrance of the Tent of Meeting, a lamb in its first year for a burnt offering, and a pigeon or a turtledove for a purgation offering.
Chabad.org — Chumash, English translation + Rashi for Vayikra 12:6
Torah Temimah cites Nazir 64b for the distinction between an event on the day the purification period is completed and an event during that period.
E-Daf — Nazir 64b · Shas.org · Sefaria — Nazir 64b, source text and translation
English: Scripture says “when the days of her purification are completed”: on the day of completion she brings; within the period of completion she does not.
Textual limitation
The timing distinction applies to an additional birth or miscarriage during a prior birth’s purification period: an event within that period does not require a separate offering, whereas one on the completion day may. This does not mean the ordinary postpartum offering is restricted to one day.