Bikkurim, Chapter 4, Mishnah 4. In this mishnah we learn the ways in which the androgynos is like both men and women - that is, the cases in which the very same halachos apply to him as apply to a man and to a woman. Some of these halachos are straightforward and self-evident.
The ways in which the androgynos is like both men and women:
"Hachovel bo v'hamekallelo" - one who wounds him and one who curses him: If the androgynos has a child, then one who strikes his parents and causes a wound with bleeding, and likewise one who curses his parents, has committed a sin punishable by death. This law applies to the mother exactly as it applies to the father, and therefore it makes no difference whether the androgynos is male or female; the halachah applies equally.
"Haholgo bishgagah goleh" - one who kills him unintentionally goes into exile: One who kills an androgynos unintentionally goes into exile, since whether one kills a man or kills a woman, the penalty is exile.
"Haholgo b'meizid neherag" - one who kills him intentionally is put to death: One who kills an androgynos intentionally is liable to death, since whether one kills a man or kills a woman, he is liable to death.
The offering of a woman after childbirth: The mother of an androgynos brings an offering after giving birth to him, just as a woman who gives birth to a boy does and just as a woman who gives birth to a girl does. The Torah says explicitly that at the end of her days of purification the mother brings an offering "for a son or for a daughter," and it is the very same offering, so there is no difference whether the child is male or female.
Eating the sanctified gifts outside the Temple: If the androgynos is the child of a kohen, we have no way to determine whether he is a man or a woman. Certain offerings that are eaten in the Beis HaMikdash may be eaten only by male kohanim; but the gifts of kehunah that are eaten outside the Temple - Terumah, terumas maaser and bikkurim - may be eaten by the daughters of kohanim as well. Therefore the androgynos may eat the sanctified gifts that are eaten outside the Temple, since both the males and the females of the kohen's family are fit to eat them.
Inheritance: The androgynos inherits both as a male and as a female. This means that when there are no other heirs standing against him - males who could claim that perhaps he is a female and therefore does not inherit according to the default rule of Torah law - he does inherit. We do not say that the androgynos is a separate creature and is not included among children; rather, he inherits from his parents in the way that sons and daughters inherit.
A closer look at the first item:
The wording of the mishnah regarding one who strikes and one who curses requires study: if we are speaking of the child of the androgynos, then the androgynos himself is the parent, whether father or mother, and his status as an androgynos has no bearing on the law at all, since one who wounds his parents or curses them is liable in any event. And indeed, in the Tosefta this case is not counted among the ways in which the androgynos is like both a man and a woman, even though in the version before us it does appear, and we have no clear answer to this question.
In summary: In this mishnah we listed the ways in which the androgynos is like both men and women: one who wounds him and one who curses him, one who kills him unintentionally and goes into exile and one who kills him intentionally and is put to death, the offering his mother brings after childbirth, his eating of the sanctified gifts outside the Temple when he is the child of a kohen, and his inheriting from his parents. In all of these his dual status is no obstacle, since the halachah is the same for a man and for a woman.