Shulchan Aruch/Even ha-Ezer/8
Any doubts about births follow the status of the male 
(Contains 5 paragraphs)
1. Cohanim, Leviim, and Yisraelim are permitted to cohabit with one another and the child retains the (ancestral) status of the man
2. Leviim, Yisraelim, and Challim (those whose father is a Cohen and whose mother is someone forbidden to Cohanim) are permitted to cohabit with one another and the child retains the (ancestral) status of the man
3. Leviim, Yisraelim, Challim, converts, and freed slaves are permitted to cohabit with one another. A male convert or freed slave who marry a female Levi, Yisraelite, of Chalilit, their son is an Yisraelite. A male Yisraelite, Levi, or Chalil who marries a female convert or freed slave, the child retains the (ancestral) status of the man.
4. Anyone who marries someone who is forbidden to them, the child retains that status of the one who has a defect. If one of them is invalid to a Cohen then the offspring (of their union) will be invalid to a Cohen. If one of them is invalid to the community of Israel (ex. a Mamzer), their offspring will be invalid to the community of Israel.
5. The child of a female maidservant, non-Jewish woman retain their status (lit. are just like them) whether or not she became pregnant in a valid way (kasher) or an invalid way (pasal)