Hi Gene,
Yes, pages 72 & 73 of the Subject Definitions doc explain all the gory details (which is pretty much why it's my favorite Census Documentation on all of census.gov).
Here's an excerpt:
Medicaid comes from 16(d) on the Questionnaire, but also some edits listed on page 72 & 73: "Medicaid or other means-tested public coverage was given to foster children, certain individuals receiving Supplementary Security Income or Public Assistance, and the spouses and children of certain Medicaid beneficiaries." as well as appropriate write-in responses for a "yes" to 16(h).
As far as public vs. private in C27002: "Respondents reporting a “yes†to the types listed in parts a, b, or e were considered to have private health insurance. Public health coverage includes the federal programs Medicare, Medicaid, and VA Health Care (provided through the Department of Veterans Affairs), as well as the Children’s Health Insurance Program (CHIP) and individual state health plans. Respondents reporting a “yes†to the types listed in c, d, or f were considered to have public coverage. The health insurance classifications are not mutually exclusive-- people may be covered by more than one at the same time."
Also keep in mind that any tabulations by sex, by age, by race/ethnicity, by labor force participation, etc. use a combination of multiple questions.