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We classify blocks in the BGG category $\mathcal O$ of modules ofnon-integral weights for the exceptional Lie superalgebra $G(3)$. We computethe characters for tilting modules of non-integral weights in $\mathcal O$.Reduction methods are established to connect non-integral blocks of $G(3)$ withblocks of the special linear Lie algebra $\mathfrak{sl}(2)$, the exceptionalLie algebra $G_2$, the general linear Lie superalgebras $\mathfrak{gl}(1|1)$,$\mathfrak{gl}(2|1)$ and the ortho-symplectic Lie superalgebra$\mathfrak{osp}(3|2)$.

Blocks and characters of $G(3)$-modules of non-integral weights