Do not reveal anything about your investigation.  It’s possible that the beating was done to conceal the poisoning.  Any false move could tip the killer off that the poison was discovered, so the timing should probably be left up to the Inspector 

It will be interesting - and noteworthy - to see if anyone tries to find out more about the autopsy. People who ask a lot of questions may know that it was more than just a beating... which means they know more about the murder than they should.