  The role of Israel-Hartle-Hawking vacuum is discussed for anomalous fluid in
presence of both the gauge and gravitational anomalies in ($1+3$) dimensions. I
show that imposition of this vacuum condition leads to the relation
$\tilde{c}_{4d}=-8\pi^2c_m$ between the response parameter ($\tilde{c}_{4d}$)
and the anomaly coefficient ($c_m$). This establishes a connection between the
coefficients appearing in a first order and a third order derivative terms in
the constitutive relation.
