The City's Annual Report for 2002 (which ended in June of 2003) says,

"Claims against the City arise out of the vast undertakings of the various City Agencies ... Generally, the cost of claims is paid out of the City's General Fund. ... HHC, the New York City Police Department and the Department of Transportation are the three entities routinely responsible for the highest judgments ..."

Addition on 9/27/04:

The New York City Law Department Tort Division page says:

"The Tort Division is the Law Department's largest. It employs over 200 lawyers and almost as many support staff. The Division represents the City, its Department of Education, and its Health and Hospitals Corp. in all tort claims. It handles this enormous caseload - 8,000 new suits each year, with another 43,000 pending - through vigorous investigation, zealous defense before State and Federal courts, and, when appropriate, settlement."

For example, one of their pages says:

"When an action is settled against THE CITY OF NEW YORK, DEPARTMENT OF EDUCATION, HEALTH AND HOSPITALS CORPORATION, or ANY NAMED INDIVIDUAL REPRESENTED BY THE CORPORATION COUNSEL, or any other defendant represented by this office, payment is conditioned upon the appropriate tender 1 of the following papers to 100 Church Street, 4th floor, New York City, New York 10007."