I don't think this is a rolling shutter issue. At first sight, this looks like motion blur or double flash on a long exposure, but flash was not used accoring to EXIF and at 1/80 s there shouldn't be that much motion blur...
Looking more closely, it seems the double image is limited to a small band in the image. I assume this is either a processing error by the camera's JPG engine or maybe a faulty SD card that left the image slightly corrupted.
Do you happen to have a RAW image, too?
Hmm, after a google search, there might actually be an eletronic shutter related issue. First of all, the slow readout of the sensor obviously does lead to image distortions. Some links to discussions adressing the issue:
A youtube video showing the heavy distortion (link from the above dpr thread):
There are also many threads pointing out severe banding issues with the electronic shutter when flickering lights, especially LED lights, are the main light source.
However, none of these explain the double exposure character we can see in Tony's sample image. I suspect a different reason: the slow readout combined with active IS. In fact, the EXIF data shows that IS was on and in panning mode (which, I think, on the EF 35/2 IS can not be set on the lens, so it was automatically selected by the camera and/or lens). I assume that during the readout of the affected part of the image the IS unit was moving, leading to the artifact that can be seen on the face in the sample... or actually in the whole image, from her hair down to her belt.
If so, the best solution should be to switch off IS when silent shutter is used and exposure times are short enough.
Personal side note: maybe I have been away from this forum for too long and simply no longer used to it, but I really don't like the subtle (or actually sometimes not very subtle) aggressive and dismissive tone in some of the posts here if someone asks for help or explanations.