This paper examines potential bias in the Census Household Composition Key's (CHCK) probabilistic parent-child linkages. By linking CHCK data to the American Community Survey (ACS), we reveal disparities in parent-child linkages among specific demographic groups and find that characteristics of children that can and cannot be linked to the CHCK vary considerably from the larger population. In particular, we find that children from low-income, less educated households and of Hispanic origin are less likely to be linked to a mother or a father in the CHCK. We also highlight some data considerations when using the CHCK.