The whole country was much more dangerous in the 70s-80s than it was in the 2000s. https://www.statista.com/statistics/187592/death-rate-from-h... NYC's peak-to-trough was bigger than the rest of the country, but it's not obvious that Giuliani was the cause, as opposed to a general trend having a more pronounced effect in the city (possibly because whatever malaise was causing the murders was more concentrated in the city). This is consistent with e.g. the lead-crime hypothesis, but there are a number of other ways that might explain the amplification of crime in the city.

Edit: Although, upon looking at this more, in NYC the decline was really pronounced at the beginning of Giuliani's tenure. I am politically predisposed to discredit Giuliani because of his more recent antics, but it's also true that bad people can sometimes accomplish good things. I looked for evidence on this topic and it does seem that the increased enforcement of crimes during Giuliani's mayorship probably had some significant effects on crime. I regret the implication that it did not, since it seems I was likely incorrect.