  In this paper, we classify all simple jet modules for the Neveu-Schwarz
algebra $\widehat{\mathfrak{k}}$ and its contact subalgebra $\mathfrak{k}^+$.
Based on these results, we give a classification of simple Harish-Chandra
modules for $\widehat{\mathfrak{k}}$ and $\mathfrak{k}^+$.
