The best resource for this information is the local police department or county sheriff's department. They have access to the mose accurate and up to date information and are generally very willing to be helpful.
There is a lot of misinformation in this forum and I would like to provide several points of clarification:
The Morningside Heights district starts on 110th street and extends only as far as the northeast corner of Morningside Drive and 125th street. One answer in this forum erroneously posted a link to the crime statistics for the 24th precinct. This is irrelevant information because the 24th precinct does not include the Morningside Heights neighborhood (the precinct's zone ends at 110th street).
Please note that it would also not be informative to look at the crime statistics for the 26th precinct which include the Morningside Heights area because it also includes a large tract of land outside the boundaries of the neighborhood where crime is (likely to be) far more prevalent. There is a significant drop in median household income above 125th street (refer to census data, e.g., http://www.wnyc.org/blogs/wnyc-news-blog/2011/dec/08/census- ). Empirical evidence suggests a close relationship between income and crime, and therefore anecdotal evidence of more crime above 125th street is probably credible. Since the neighborhood terminates at 125th street, crime above 125th street should be excluded from the 26th precinct's data if the objective is to characterize the Morningside Heights neighborhood.
Columbia university has their own security force which patrols the neighborhood. Under cover detectives and unmarked police cars are constantly patrolling the area.
Please refer to this crime map of NYC which indicates that Morningside Heights as the 2nd lowest crime rate in all of manhattan. http://www.morningside-heights.net/crime.htm