  We carry out relativistic many-body calculations of the Stark-induced
absorption coefficient on the 254-nm $6s6p ^3P_1 (F=1/2) - 6s^2 ^1S_0$ line of
$^{199}$Hg atom, the effect considered before by Lamoreaux and Fortson using a
simple central field estimate [Phys. Rev. A {\bf 46}, 7053 (1992)]. The
Stark-induced admixing of states of opposite parity opens additional M1 and E2
transition channels. We find that the resulting M1-E1 absorption dominates over
E2-E1 absorption. The value of the E2-E1 absorption coefficient depends
strongly on the details of treatment of the correlation problem. As a result,
our numerical values differ substantially from those of the earlier central
field calculation. Reliable calculation of this effect can enable a useful
experimental check on the optical technique being used to search for a
permanent electric dipole moment of the $^{199}$Hg atom.
