Judging from the experience of African Americans do you see a correlation between race, class and access to medical care in the USA?
The research would say yes, African Americans don't have the same access to health care services as do white Americans, regardless of economic status. A report issued by Johns Hopkins University (http://books.nap.edu/openbook.php?isbn=030908265X) entitled Unequal Treatment: Confronting Racial and Ethnic Disparities in Health Care addresses your question quite directly.
The study identifies basic environmental factors that impact the provision of health care services to minority populations including:
the historical evolution of healthcare for persons of color, the current financial and organizational structures of health care systems, the settings in which care is delivered, and the nature of the workforce providing care
Going back in history to the services given to slaves (minimal, only to preserve their ability to work), including the connection between ability to pay and access to care, encompassing the tensions dating back to segregated facilities and providers with less training and equipment to use in diagnosing and treating medical conditions - there are a multitude of causative reasons all leading to a direct correlation between race and access to health care.