  We investigate the first cohomology space associated with the embedding of
the Lie superalgebra $\cK(2)$ of contact vector fields on the (1,2)-dimensional
supercircle $S^{1\mid 2}$ in the Lie superalgebra $\cS\Psi \cD \cO(S^{1\mid
2})$ of superpseudodifferential operators with smooth coefficients. Following
Ovsienko and Roger, we show that this space is ten-dimensional with only even
cocycles and we give explicit expressions of the basis cocycles.
