  Let $(S,L)$ be a Lie-Rinehart algebra such that $L$ is $S$-projective and let
$U$ be its universal enveloping algebra. In this paper we present a spectral
sequence which converges to the Hochschild cohomology of $U$ with values on a
$U$-bimodule $M$ and whose second page involves the Lie-Rinehart cohomology of
the algebra and the Hochschild cohomology of $S$ with values on $M$. After
giving a convenient description of the involved algebraic structures we use the
spectral sequence to compute explicitly the Hochschild cohomology of the
algebra of differential operators tangent to a central arrangement of three
lines.
