  We derive the solutions of the boundary Yang-Baxter equation associated with
a supersymmetric nineteen vertex model constructed from the three-dimensional
representation of the twisted quantum affine Lie superalgebra
$U_{q}[\mathrm{osp}\left(2|2\right)^{\left(2\right)}]\simeq
U_{q}[C\left(2\right)^{\left(2\right)}]$. We found three classes of solutions.
The type I solution is characterized by three boundary free-parameters and all
elements of the corresponding reflection $K$-matrix are different from zero. In
the type II solution, the reflection $K$-matrix is even (every element of the
$K$-matrix with an odd parity is null) and it has only one boundary
free-parameter. Finally, the type III solution corresponds to a diagonal
reflection $K$-matrix with two boundary free-parameters.
