What happens is not due to some stickiness inherent to electricity, but rather, the electric shock causes your muscles to involuntarily contract. If you're unlucky, such a contraction could effect a firm grip around the electric source, which would render you unable to let go of it.
All about circuits elaborates:
> The forearm muscles responsible for bending fingers tend to be better developed than those muscles responsible for extending fingers, and so if both sets of muscles try to contract because of an electric current conducted through the person's arm, the "bending" muscles will win, clenching the fingers into a fist. If the conductor delivering current to the victim faces the palm of his or her hand, this clenching action will force the hand to grasp the wire firmly, thus worsening the situation by securing excellent contact with the wire. The victim will be completely unable to let go of the wire.