  In this paper, we extend the definition of the $SL_2(\Bbb C)$ Casson
invariant to arbitrary knots $K$ in integral homology 3-spheres and relate it
to the $m$-degree of the $\widehat{A}$-polynomial of $K$. We prove a product
formula for the $\widehat{A}$-polynomial of the connected sum $K_1 \# K_2$ of
two knots in $S^3$ and deduce additivity of $SL_2(\Bbb C)$ Casson knot
invariant under connected sum for a large class of knots in $S^3$. We also
present an example of a nontrivial knot $K$ in $S^3$ with trivial
$\widehat{A}$-polynomial and trivial $SL_2(\Bbb C)$ Casson knot invariant,
showing that neither of these invariants detect the unknot.
