In this work, we extend the uni-dimensional results, already found by Jerbi and Kharrat, for the multidimensional case: we compute the Malliavin weights related to the conditional expectation $\mathbb{E}(P_{t}(X_{t})|(X_{s}))$ for $0 \leq s \leq t$, where the only state variable follows a multidimensional J-process.