The capacitor provides a path for high frequency AC.
It should be a small enough value that you cannot feel the current flow.
Sometimes, the capacitor is placed on the AC input side of the common mode choke. Sometimes, a common mode choke is also needed on the secondary side. The exact combination of chokes and capacitors, and their placement, is hard to figure out until testing.
If you have a three-prong AC cord, the neutral wire should be consistent, and a capacitor to neutral should not deliver any ground leakage current. This would be a better location than across the transformer.
Tim