  A Poincar\'e type K\"ahler metric on the complement X\D of a simple normal
crossing divisor D, in a compact K\"ahler manifold X, is a K\"ahler metric on
X\D with cusp singularity along D. We relate the Futaki character for
holomorphic vector fields parallel to the divisor, defined for any fixed
Poincar\'e type K\"ahler class, to the classical Futaki character for the
relative smooth class. As an application we express a numerical obstruction to
the existence of extremal Poincar\'e type K\"ahler metrics, in terms of mean
scalar curvatures and Futaki characters.
