Does she need to have testicles to produce testosterone, right?
All people have both testosterone, the male “sex hormone” and estrogen, the female "sex hormone. They just produce it different quantities. Both are needed for all people.
There are a lot of very normal and quite frequent medical reasons why a person’s hormone levels can be mixed up and for a woman (afab) to have a high testosterone level or for a man (amab) a high estrogen level.
Women (XX) produce testosterone in mostly their ovaries and adrenal glands.
Men (XY) synthesize estrogen in the Leydig cells and the germ cells in their testis.
You seem to be under the false impression that women’s bodies don’t produce testosterone under normal circumstances. They do. Women produce testosterone in their ovaries, adrenal glands, fat and skin cells.
This is true, but they do not produce it in the same quantity as testicles do in males.
I know that but usually women produce less testosterone, is it related the XY chromosomes to the production of testosterone?
I doubt any statistically significant study has been done since XY females are rare. In men the adrenal glands produce only 5-10% of total testosterone. In women the ovaries and adrenal glands make most of it, so I’d expect an XY woman with ovaries to have fairly normal levels. If she has no ovaries then I’d expect the level to be low. It’s about having the organs that do the production, not about the chromosomes.
That said, people vary A LOT so you’ll find an edge case for almost anything you look for.
What’s the context of your question?
The Olympic boxer thing.
There’s no evidence she’s XY. A butthurt Russian boxing official’s claim doesn’t count as evidence.