Yes, it would make sense that he poisoned his otherwise relatively healthy white grandmother. She was found dead a short time after his sudden and unexpected visit and was reported in ill health in the media although this was contradicted by others who knew her. He wouldn't want her blurting out uncomfortable truths during his presidency, such as his real birthplace. Unfortunately there is no physical evidence to have an autopsy or analysis, so it'll always be up for conjecture. If there's no evidence, no witnesses and he doesn't admit it, then there's no case, but I wouldn't put it past him.