We study contact process with random recovery rates ξ$\xi$ and edge weights ρ$\rho$ on tree T^N${\mathbb{T}}^N$.

We introduce the definitions of the critical values under the annealed and quenched measures.

We show that the critical value under the annealed measure asymptotically equals ${\left(NE\rho E\frac{1}{\xi }\right)}^{-1}$ as N$N$ grows to infinity.

We show that the critical value under the quenched measure equals that under the annealed measure on a set A$A$ and equals infinity on the complement of A$A$.