  In this article, we prove that a tunnel number two knot induces a critical
Heegaard splitting in its exterior if there are two weak reducing pairs such
that each weak reducing pair contains the cocore disk of each tunnel. Moreover,
we prove that a connected sum of two 2-bridge knots or more generally that of
two $(1,1)$-knots can induce a critical Heegaard splitting in its exterior as
the examples of the main theorem. Finally, we give an equivalent condition for
a weak reducing pair to be determined by a compressing disk uniquely when the
manifold is closed, irreducible and the Heegaard splitting is of genus three
and unstabilized.
