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We derive the solutions of the boundary Yang-Baxter equation associated witha supersymmetric nineteen vertex model constructed from the three-dimensionalrepresentation of the twisted quantum affine Lie superalgebra$U_{q}[\mathrm{osp}\left(2|2\right)^{\left(2\right)}]\simeqU_{q}[C\left(2\right)^{\left(2\right)}]$. We found three classes of solutions.The type I solution is characterized by three boundary free-parameters and allelements of the corresponding reflection $K$-matrix are different from zero. Inthe 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 boundaryfree-parameter. Finally, the type III solution corresponds to a diagonalreflection $K$-matrix with two boundary free-parameters.

Reflection $K$-matrices for a nineteen vertex model with $U_{q}[\mathrm{osp}\left(2|2\right)^{\left(2\right)}]$ symmetry