Complete data is filled out for each person.
The instructions do states that whoever is owns, is buying or renting the house should be one of the first two people identified. If nobody in the household is renting, owns or is buying the house, then any adult can answer first. You can mark more than one box if you feel you identify with more than one race. While this possibility might seem to hurt Native Americans because mixed bloods who truly are part of a tribal community might feel they should report their mixed heritage, it might also help, because people who are of limited heritage who might otherwise not feel honest about reporting themselves as Native American might claim that heritage if they could indicate it as a mixture. So each individual in your household will have an opportunity to have their heritage listed on this census.