  We show that the Painlev\'{e} test is useful not only for probing
(non-)integrability but also for finding the values of spins of conserved
currents (W currents) in Toda field theories (TFTs). In the case of the TFTs
based on simple Lie algebras the locations of resonances are shown to give
precisely the spins of conserved W currents. We apply this test to TFTs based
on strictly hyperbolic Kac-Moody algebras and show that there exist no
resonances other than that at n=2, which corresponds to the energy-momentum
tensor, indicating their non-integrability. We also check by direct calculation
that there are no spin-3 nor -4 conserved currents for all the hyperbolic TFTs
in agreement with the result of our Painlev\'{e} analysis.
