  Trigonal curves provide an example of Brill-Noether special curves. Theorem
1.3 of [9] characterizes the Brill-Noether theory of general trigonal curves
and the refined stratification by Brill-Noether splitting loci, which
parametrize line bundles whose push forward to $\mathbb{P}^1$ has a specified
splitting type. This note describes the refined stratification for all trigonal
curves. Given the Maroni invariant of a trigonal curve, we determine the
dimensions of all Brill-Noether splitting loci and describe their irreducible
components. When the dimension is positive, these loci are connected, and if
furthermore the Maroni invariant is $0$ or $1$, they are irreducible.
