Dorman's paper on singular moduli uses the "local character given by class field theory". Specifically, on page 178, the author states,
For each prime $p$, finite or infinite, let $\epsilon_p : \mathbb{Q}_p(\sqrt{d}) \to \{\pm 1\}$ be the local character given by class field theory.
I'm familiar with the main statements of class field theory, but I have to admit - I don't know what this character is. Can anyone enlighten me with a reference?