In short: No, it is not possible to give a hypnotic suggestion (post-hypnotic or during the hypnosis session) to convince someone to kill another person... except to the extent that it is possible to convince people to perform remarkably antisocial, dangerous or objectionable activities stuff even without hypnosis.
Here are three summaries of the evidence:
A 2001 report from the British Psychological Society, The Nature of Hypnosis summarised:
Hypnosis and will
Hypnotic procedures are not in themselves able to cause people to commit acts against their will.
However, the demands of the context in which the procedures take place may exert pressure on the
subject to comply with the hypnotist’s instructions.
Aside from studies on the coercive nature of the psychological experiment itself, evidence for the above assertions
comes from studies on hypnosis by Levitt et al. (1975), O’Brian & Rabuck (1976) and Orne & Evans (1965).
It follows that any allegation that hypnosis caused a person to engage in activities against his or her will must be assessed
from a careful consideration of non-hypnotic influences present in the context (Heap, 1995a; Hoëncamp, 1989; Orne, 1972).
The Oxford Handbook of Hypnosis: Theory, Research and Practice introduces the term "hyperobedience" and draws similar conclusions from similar sources (page 748):
From a modern theoretical perspective, it is difficult to make the case that hyperobedience is a property of hypnosis, even in highly hypnotizable people. The modern theory that may be most relevant to this issue is the dissociated control model due to Woody and Bowers (1994). This theory proposes that during hypnosis the influence of the supervisory attention system of the frontal lobes is suppressed and the subject's responding is governed by 'contention scheduling' in the same manner as other behaviour that is habitually executed in an automatic fashion.
In fact, laboratory studies (e.g. Orne and Evans, 1965; Coe et al., 1972, Levit et al, 1975; O'Brian and Rabuck, 1976) have compared hypnotic and control subjects in their willingness, amongst other things, to make slanderous statements, plunge their hands in a beaker containing 'acid' and throw 'acid' at the experimenter, mutilate the bible, cut up the national flag, make homosexual advances, steal, and deal in heroin, and no convincing evidence has emerged to indicate that hypnotic subjects are more likely to obey such instructions than control subjects who are subjected to the same demands and pressures.
The experiments of Milgram (1974) may be particularly apposite here.
The American Society of Clinical Hypnosis provides no references, but concur in their website's FAQ:
You are in control and cannot be made to do anything against your will.
One common misconsception is that a hypnotized person loses their will and is partially or completely under the command of the hypnotist. Nothing could be further from the truth. This unfortunate belief is reinforced by many stage hypnotists. You are in control of yourself, and cannot be made to do anything that is against your will.
The above references were a bit theoretical and high-level - I want to see some experimental data, so I tried chasing down some of the references they provided.
This paper does not attempt to "answer the question whether antisocial behavior can be elicited under hypnosis". However, it demonstrates that previous experiments suggesting they could were flawed, due to lack of controls. That is the control groups were also likely to reach into pick up (apparently) dangerous snakes or throw 'acid' in people's faces, if they were subject to equivalent social pressures.
we still have not found an aspect of behavior which is sufficiently safe to request of a subject, and which a subject will refuse to carry out if the expectation of compliance is communicated to him. In the present study the experimenter could virtually predetermine the nature of the resulting behavior by deciding in advance whether he would consciously, but subtly, communicate to a subject an expectation either of failure or of compliance.
(Note: This is about hypnotic suggestion rather than post-hypnotic suggestion. I am assuming that hypnotic suggestions are stronger, making the post-hypnotic case moot.)
One of the authors explores this issue further:
It would appear that attempts to answer the question whether an individual can or cannot be compelled to carry out antisocial actions or, for that matter, actions against his will, transcend the limitations of the experimental situation. Very subtle factors in the manner in which the experiments are conducted will yield different and contradictory results. Ecologically valid answers to these basic questions can be obtained only in contexts that are not perceived to be experimental, since the subject's awareness that he is participating in the study drastically alters his perception of the situation
[...]
In fact, no authority has seriously maintained that such a total control fantasy could be translated into real life with the help of hypnosis. Fortunately, the Manchurian Candidate still remains fiction.
Having said that, he goes on to list cases of hypnotists being accused of triggering unacceptable behaviour from patients. Again, these anecdotes don't prove the same behaviour wouldn't have been also conjured up by a non-hypnotic suggestion.
This would be a good point to introduce:
This author lists case studies of times that hypnotists have been accused of using hypnosis to take advantage of their patients (including for sexual assault). He explains the processes that should be used to evaluate these cases. In general, the question of whether this same behaviour would have been elicited with hypnosis remains critical.
I tried to look up some more studies:
- Levitt, E.E. Aronoff, G., Morgan, C.D., Overly, T.M., & Parrish, M.J. (1975). Testing the coercive
power of hypnosis: Committing objectionable acts. International Journal of Clinical and Experimental
Hypnosis, 23, 59-67, DOI:10.1080/00207147508416173
This wasn't terribly useful, just showing that you could measure objectionable, rather than criminal or dangerous, acts to measure the power of hypnosis.
I couldn't even find an abstract of these two papers not hidden behind a paywall. Shame. Anyone with access want to summarise?
In conclusion:
It is difficult to prove that negative post-hypnotic suggestions couldn't exist, but well-controlled experimental attempts to show that they exist have failed. A key way that they have failed is that control groups of non-hypnotised people people trust experimenters, and follow their suggestions even when it would seem objectionable or dangerous.
This makes particular anecdotes difficult to assess (whether it is allegations of sexual assault under hypnosis, or the apparent willingness of a participant to shoot a gun at another person, as reported by the CIA) as they may well have been willing to comply with an authority to commit such acts without being hypnotised.