  Let $X \subset\mathbb{P}^r$ be a projective $d$-variety with isolated
determinantal singularities and $\omega$ be a $1$-form on $X$ with a finite
number of singularities (in the stratified sense). Under some technical
conditions on $r$ we use two generalization of Poincar\'e-Hopf index with the
goal of proving a Poincar\'e-Hopf Type Theorem for $X$.
