What is the ruling regarding the use of perfumes during menstruation? Is it permissible to use perfumes during it?
There's a bunch of ahadith that restrict the usage of perfumes. Relevant to women are notably:
It was narrated that Al-Ash'ari said: "The Messenger of Allah [SAW] said: 'Any woman who puts on perfume then passes by people so that they can smell her fragrance then she is an adulteress.'" -- Sunan an-Nasa'i 5126 [grade: hasan] (sunnah.com)
It was narrated that Abu Hurairah said: "The Messenger of Allah [SAW] said: 'If a woman has perfumed herself with incense, let her not attend 'Isha' prayer.'" -- Sunan an-Nasa'i 5128 [grade: sahih] (sunnah.com)
There's also a difference of scholarly opinion concerning alcohol in perfumes, based on whether alcohol is impure [and not just forbidden as an intoxicant] (see Islamic Centre).
Thus, I suspect the OP thinks that perfumes are generally either forbidden or discouraged based on the above, and thus is asking if it's still forbidden/discouraged during menstruation. However, the default stance with perfumes is permissibility.
There are ways to misuse perfumes which are forbidden, e.g., with the intention of letting non-mahram men smell it (Islam Q&A fatwa 102329), and when attending mosque (Islam Q&A fatwa 7850). These apply whether or not a woman is menstruating.
There's even the hadith:
It was narrated from 'Aishah that: Asma asked the Messenger of Allah about bathing after ones's period. He said: "... Then she should take a piece of cotton perfumed with musk and purify herself with it." ... -- Sunan Ibn Majah [grade: sahih] (sunnah.com)
which has been interpreted as encouraging perfuming during menstruation:
The reason for using this is to perfume the site and ward off unpleasant odours. -- Islam Q&A