Self-driving cars have the potential to greatly improve public safety. However, their introduction onto public roads must overcome both ethical and technical challenges. To further understand the ethical issues of introducing self-driving cars, we conducted two moral judgement studies investigating potential differences in the moral norms applied to human drivers and self-driving cars. In the experiments, participants made judgements on a series of dilemma situations involving human drivers or self-driving cars. We manipulated which perspective situations were presented from in order to ascertain the effect of perspective on moral judgements. Two main findings were apparent from the results of the experiments. First, human drivers and self-driving cars were largely judged similarly. However, there was a stronger tendency to prefer self-driving cars to act in ways to minimize harm, compared to human drivers. Second, there was an indication that perspective influences judgements in some situations. Specifically, when considering situations from the perspective of a pedestrian, people preferred actions that would endanger car occupants instead of themselves. However, they did not show such a self-preservation tendency when the alternative was to endanger other pedestrians to save themselves. This effect was more prevalent for judgements on human drivers than self-driving cars. Overall, the results extend and agree with previous research, again contradicting existing ethical guidelines for self-driving car decision making and highlighting the difficulties with adapting public opinion to decision making algorithms.