The way I read the article that vieome referred to is that it was NOT the cleaning up of the neighbourhood but police presence that made the difference.

Nevertheless, a close look at the data after 2000 does point to the importance of policing. In spite of the loss of 4,000 officers, the most recent period still has substantially more police on the street compared with 1990.
Had the city followed through on its broken-windows policing, it would have concentrated precious resources in marginal neighborhoods rather than in those with the highest crime. In fact, the police did the opposite: they emphasized ‘hotspots’ a strategy that had been proved effective in other cities and that almost certainly made a substantial contribution in New York.