Parity violation potential

I read in several papers (e.g. this one) that if we have 2 levels of fixed, opposite parities, which are the eigenstates of a $P$,$T$-even Hamiltonian, and we add a perturbing potential which is $P$-odd, $T$-even, the matrix element of the new potential between the 2 states of opposite parity must be purely imaginary. How can I prove this?