Level crossings of Stark substates with m = 0 differing in reflection parity are considered with respect to the detection of parity violation in atomic physics. An interesting example of a 0⁺-0^- crossing occurs in the electric-field splitting of the 1s 3d levels of ⁴He I at 80 kV/cm. Experiments are proposed allowing the detection of parity violation by studying the radiative decay of the 0^- state into singlet levels. By observing circularly polarized light, constructive and destructive interference between transitions induced by weak interactions and by an external magnetic field can be observed at the 0⁺-0^- crossing.