  We present measurements of Stark interference in the 6$^1S_0$ $\rightarrow$
6$^3P_1$ transition in $^{199}$Hg, a process whereby a static electric field
$E$ mixes magnetic dipole and electric quadrupole couplings into an electric
dipole transition, leading to $E$-linear energy shifts similar to those
produced by a permanent atomic electric dipole moment (EDM). The measured
interference amplitude, $a_{SI}$ = $(a_{M1} + a_{E2})$ = (5.8 $\pm$ 1.5)$\times
10^{-9}$ (kV/cm)$^{-1}$, agrees with relativistic, many-body predictions and
confirms that earlier central-field estimates are a factor of 10 too large.
More importantly, this study validates the capability of the $^{199}$Hg EDM
search apparatus to resolve non-trivial, controlled, and sub-nHz Larmor
frequency shifts with EDM-like characteristics.
