The Supreme Court case you're looking for is:
South v. Maryland, 59 U.S. (18 How.) 396 (1855)
One of the most recent S.Ct. cases affirming "no duty to protect" is:
DeShaney v. Winnebago County Department of Social Services, 489 U.S. 189 (1989)
Look at the cites within those cases for various state case references.