  Using the matrix-resolvent method and a formula of the second-named author on
the $n$-point function for a KP tau-function, we show that the tau-function of
an arbitrary solution to the Toda lattice hierarchy is a KP tau-function. We
then generalize this result to tau-functions for the extended Toda hierarchy
(ETH) by developing the matrix-resolvent method for the ETH. As an example the
partition function of Gromov--Witten invariants of the complex projective line
is a KP tau-function, and an application on irreducible representations of the
symmetric group is obtained.
